Bibliography G
-
B. Gabutti and G. Allasia (2008)
Evaluation of
-gamma function and -analogues by iterative algorithms.
Numer. Algorithms 49 (1-4), pp. 159–168.
-
B. Gabutti and B. Minetti (1981)
A new application of the discrete Laguerre polynomials in the numerical evaluation of the Hankel transform of a strongly decreasing even function.
J. Comput. Phys. 42 (2), pp. 277–287.
-
B. Gabutti (1979)
On high precision methods for computing integrals involving Bessel functions.
Math. Comp. 33 (147), pp. 1049–1057.
-
B. Gabutti (1980)
On the generalization of a method for computing Bessel function integrals.
J. Comput. Appl. Math. 6 (2), pp. 167–168.
-
E. A. Galapon and K. M. L. Martinez (2014)
Exactification of the Poincaré asymptotic expansion of the Hankel integral: spectacularly accurate asymptotic expansions and non-asymptotic scales.
Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 470 (2162), pp. 20130529, 16.
-
B. Gambier (1910)
Sur les équations différentielles du second ordre et du premier degré dont l’intégrale générale est a points critiques fixes.
Acta Math. 33 (1), pp. 1–55.
-
L. Gammaitoni, P. Hanggi, P. Jung, and F. Marchesoni (1998)
Stochastic resonance.
Rev. Modern Phys. 70 (1), pp. 223–287.
-
M. J. Gander and A. H. Karp (2001)
Stable computation of high order Gauss quadrature rules using discretization for measures in radiation transfer.
J. Quant. Spectrosc. Radiat. Transfer 68 (2), pp. 213–223.
-
F. Gao and V. J. W. Guo (2013)
Contiguous relations and summation and transformation formulae for basic hypergeometric series.
J. Difference Equ. Appl. 19 (12), pp. 2029–2042.
-
GAP (website)
The GAP Group, Centre for Interdisciplinary Research in Computational Algebra,
University of St. Andrews, United Kingdom.
-
R. D. M. Garashchuk and J. C. Light (2001)
Quasirandom distributed bases for bound problems.
J. Chem. Phys. 114 (9), pp. 3929–3939.
-
L. Gårding (1947)
The solution of Cauchy’s problem for two totally hyperbolic linear differential equations by means of Riesz integrals.
Ann. of Math. (2) 48 (4), pp. 785–826.
-
I. Gargantini and P. Henrici (1967)
A continued fraction algorithm for the computation of higher transcendental functions in the complex plane.
Math. Comp. 21 (97), pp. 18–29.
-
F. G. Garvan and M. E. H. Ismail (Eds.) (2001)
Symbolic Computation, Number Theory, Special Functions, Physics and Combinatorics.
Developments in Mathematics, Vol. 4, Kluwer Academic Publishers, Dordrecht.
-
G. Gasper and M. Rahman (1990)
Basic Hypergeometric Series.
Encyclopedia of Mathematics and its Applications, Vol. 35, Cambridge University Press, Cambridge.
-
G. Gasper and M. Rahman (2004)
Basic Hypergeometric Series.
Second edition, Encyclopedia of Mathematics and its Applications, Vol. 96, Cambridge University Press, Cambridge.
-
G. Gasper (1972)
An inequality of Turán type for Jacobi polynomials.
Proc. Amer. Math. Soc. 32, pp. 435–439.
-
G. Gasper (1975)
Formulas of the Dirichlet-Mehler Type.
In Fractional Calculus and its Applications, B. Ross (Ed.),
Lecture Notes in Math., Vol. 457, pp. 207–215.
-
G. Gasper (1977)
Positive sums of the classical orthogonal polynomials.
SIAM J. Math. Anal. 8 (3), pp. 423–447.
-
G. Gasper (1981)
Orthogonality of certain functions with respect to complex valued weights.
Canad. J. Math. 33 (5), pp. 1261–1270.
-
L. Gatteschi (1987)
New inequalities for the zeros of Jacobi polynomials.
SIAM J. Math. Anal. 18 (6), pp. 1549–1562.
-
L. Gatteschi (1990)
New inequalities for the zeros of confluent hypergeometric functions.
In Asymptotic and computational analysis (Winnipeg, MB, 1989),
pp. 175–192.
-
L. Gatteschi (2002)
Asymptotics and bounds for the zeros of Laguerre polynomials: A survey.
J. Comput. Appl. Math. 144 (1-2), pp. 7–27.
-
M. Gaudin (1983)
La fonction d’onde de Bethe.
Masson, Paris (French).
-
J. A. Gaunt (1929)
The triplets of helium.
Philos. Trans. Roy. Soc. London Ser. A 228, pp. 151–196.
-
R. E. Gaunt (2014)
Inequalities for modified Bessel functions and their integrals.
J. Math. Anal. Appl. 420 (1), pp. 373–386.
-
C. F. Gauss (1863)
Werke. Band II.
pp. 436–447 (German).
-
W. Gautschi (1964a)
Algorithm 222: Incomplete beta function ratios.
Comm. ACM 7 (3), pp. 143–144.
-
W. Gautschi (1964b)
Algorithm 236: Bessel functions of the first kind.
Comm. ACM 7 (8), pp. 479–480.
-
W. Gautschi (1965)
Algorithm 259: Legendre functions for arguments larger than one.
Comm. ACM 8 (8), pp. 488–492.
-
W. Gautschi (1966)
Algorithm 292: Regular Coulomb wave functions.
Comm. ACM 9 (11), pp. 793–795.
-
W. Gautschi (1969)
Algorithm 363: Complex error function.
Comm. ACM 12 (11), pp. 635.
-
W. Gautschi (1973)
Algorithm 471: Exponential integrals.
Comm. ACM 16 (12), pp. 761–763.
-
W. Gautschi (1977a)
Evaluation of the repeated integrals of the coerror function.
ACM Trans. Math. Software 3, pp. 240–252.
-
W. Gautschi (1977b)
Algorithm 521: Repeated integrals of the coerror function.
ACM Trans. Math. Software 3, pp. 301–302.
-
W. Gautschi (1979a)
Algorithm 542: Incomplete gamma functions.
ACM Trans. Math. Software 5 (4), pp. 482–489.
-
W. Gautschi (1994)
Algorithm 726: ORTHPOL — a package of routines for generating orthogonal polynomials and Gauss-type quadrature rules.
ACM Trans. Math. Software 20 (1), pp. 21–62.
-
W. Gautschi and J. Slavik (1978)
On the computation of modified Bessel function ratios.
Math. Comp. 32 (143), pp. 865–875.
-
W. Gautschi (1959a)
Exponential integral
for large values of 
.
J. Res. Nat. Bur. Standards 62, pp. 123–125.
-
W. Gautschi (1959b)
Some elementary inequalities relating to the gamma and incomplete gamma function.
J. Math. Phys. 38 (1), pp. 77–81.
-
W. Gautschi (1961)
Recursive computation of the repeated integrals of the error function.
Math. Comp. 15 (75), pp. 227–232.
-
W. Gautschi (1967)
Computational aspects of three-term recurrence relations.
SIAM Rev. 9 (1), pp. 24–82.
-
W. Gautschi (1968)
Construction of Gauss-Christoffel quadrature formulas.
Math. Comp. 22, pp. 251–270.
-
W. Gautschi (1970)
Efficient computation of the complex error function.
SIAM J. Numer. Anal. 7 (1), pp. 187–198.
-
W. Gautschi (1974)
A harmonic mean inequality for the gamma function.
SIAM J. Math. Anal. 5 (2), pp. 278–281.
-
W. Gautschi (1975)
Computational Methods in Special Functions – A Survey.
In Theory and Application of Special Functions (Proc. Advanced
Sem., Math. Res. Center, Univ. Wisconsin, Madison, Wis.,
1975), R. A. Askey (Ed.),
pp. 1–98. Math. Res. Center, Univ. Wisconsin Publ., No. 35.
-
W. Gautschi (1979b)
A computational procedure for incomplete gamma functions.
ACM Trans. Math. Software 5 (4), pp. 466–481.
-
W. Gautschi (1979c)
Un procedimento di calcolo per le funzioni gamma incomplete.
Rend. Sem. Mat. Univ. Politec. Torino 37 (1), pp. 1–9 (Italian).
-
W. Gautschi (1983)
How and how not to check Gaussian quadrature formulae.
BIT 23 (2), pp. 209–216.
-
W. Gautschi (1984)
Questions of Numerical Condition Related to Polynomials.
In Studies in Numerical Analysis, G. H. Golub (Ed.),
pp. 140–177.
-
W. Gautschi (1992)
On mean convergence of extended Lagrange interpolation.
J. Comput. Appl. Math. 43 (1-2), pp. 19–35.
-
W. Gautschi (1993)
On the computation of generalized Fermi-Dirac and Bose-Einstein integrals.
Comput. Phys. Comm. 74 (2), pp. 233–238.
-
W. Gautschi (1996)
Orthogonal Polynomials: Applications and Computation.
In Acta Numerica, 1996, A. Iserles (Ed.),
Acta Numerica, Vol. 5, pp. 45–119.
-
W. Gautschi (1997a)
Numerical Analysis. An Introduction.
Birkhäuser Boston Inc., Boston, MA.
-
W. Gautschi (1997b)
The Computation of Special Functions by Linear Difference Equations.
In Advances in Difference Equations (Veszprém, 1995), S. Elaydi, I. Győri, and G. Ladas (Eds.),
pp. 213–243.
-
W. Gautschi (1998)
The incomplete gamma functions since Tricomi.
In Tricomi’s Ideas and Contemporary Applied Mathematics
(Rome/Turin, 1997),
Atti Convegni Lincei, Vol. 147, pp. 203–237.
-
W. Gautschi (1999)
A note on the recursive calculation of incomplete gamma functions.
ACM Trans. Math. Software 25 (1), pp. 101–107.
-
W. Gautschi (2002a)
Computation of Bessel and Airy functions and of related Gaussian quadrature formulae.
BIT 42 (1), pp. 110–118.
-
W. Gautschi (2002b)
Gauss quadrature approximations to hypergeometric and confluent hypergeometric functions.
J. Comput. Appl. Math. 139 (1), pp. 173–187.
-
W. Gautschi (2004)
Orthogonal Polynomials: Computation and Approximation.
Numerical Mathematics and Scientific Computation, Oxford University Press, New York.
-
W. Gautschi (2009)
Variable-precision recurrence coefficients for nonstandard orthogonal polynomials.
Numer. Algorithms 52 (3), pp. 409–418.
-
W. Gautschi (2016)
Algorithm 957: evaluation of the repeated integral of the coerror function by half-range Gauss-Hermite quadrature.
ACM Trans. Math. Softw. 42 (1), pp. 9:1–9:10.
-
M. Gavrila (1967)
Elastic scattering of photons by a hydrogen atom.
Phys. Rev. 163 (1), pp. 147–155.
-
I. M. Gel’fand and G. E. Shilov (1964)
Generalized Functions. Vol. 1: Properties and Operations.
Academic Press, New York.
-
M. Geller and E. W. Ng (1969)
A table of integrals of the exponential integral.
J. Res. Nat. Bur. Standards Sect. B 73B, pp. 191–210.
-
M. Geller and E. W. Ng (1971)
A table of integrals of the error function. II. Additions and corrections.
J. Res. Nat. Bur. Standards Sect. B 75B, pp. 149–163.
-
V. X. Genest, L. Vinet, and A. Zhedanov (2016)
The non-symmetric Wilson polynomials are the Bannai-Ito polynomials.
Proc. Amer. Math. Soc. 144 (12), pp. 5217–5226.
-
K. Germey (1964)
Die Beugung einer ebenen elektromanetischen Welle an zwei parallelen unendlich langen idealleitenden Zylindern von elliptischem Querschnitt.
Ann. Physik (7) 468, pp. 237–251 (German).
-
J. S. Geronimo, O. Bruno, and W. Van Assche (2004)
WKB and turning point theory for second-order difference equations.
In Spectral Methods for Operators of Mathematical Physics,
Oper. Theory Adv. Appl., Vol. 154, pp. 101–138.
-
A. Gervois and H. Navelet (1984)
Some integrals involving three Bessel functions when their arguments satisfy the triangle inequalities.
J. Math. Phys. 25 (11), pp. 3350–3356.
-
A. Gervois and H. Navelet (1985a)
Integrals of three Bessel functions and Legendre functions. I.
J. Math. Phys. 26 (4), pp. 633–644.
-
A. Gervois and H. Navelet (1985b)
Integrals of three Bessel functions and Legendre functions. II.
J. Math. Phys. 26 (4), pp. 645–655.
-
A. Gervois and H. Navelet (1986a)
Some integrals involving three modified Bessel functions. I.
J. Math. Phys. 27 (3), pp. 682–687.
-
A. Gervois and H. Navelet (1986b)
Some integrals involving three modified Bessel functions. II.
J. Math. Phys. 27 (3), pp. 688–695.
-
I. M. Gessel (2003)
Applications of the classical umbral calculus.
Algebra Universalis 49 (4), pp. 397–434.
-
P. Gianni, M. Seppälä, R. Silhol, and B. Trager (1998)
Riemann surfaces, plane algebraic curves and their period matrices.
J. Symbolic Comput. 26 (6), pp. 789–803.
-
A. G. Gibbs (1973)
Problem 72-21, Laplace transforms of Airy functions.
SIAM Rev. 15 (4), pp. 796–798.
-
A. Gibbs, D. P. Hewett, and D. Huybrechs (2024)
Numerical evaluation of oscillatory integrals via automated steepest descent contour deformation.
J. Comput. Phys. 501, pp. Paper No. 112787, 23.
-
A. Gibbs (2025)
PathFinder: A Matlab/Octave package for oscillatory integration.
Journal of Open Source Software 10 (114), pp. 6902.
-
A. Gil and J. Segura (1997)
Evaluation of Legendre functions of argument greater than one.
Comput. Phys. Comm. 105 (2-3), pp. 273–283.
-
A. Gil and J. Segura (1998)
A code to evaluate prolate and oblate spheroidal harmonics.
Comput. Phys. Comm. 108 (2-3), pp. 267–278.
-
A. Gil and J. Segura (2000)
Evaluation of toroidal harmonics.
Comput. Phys. Comm. 124 (1), pp. 104–122.
-
A. Gil and J. Segura (2001)
DTORH3 2.0: A new version of a computer program for the evaluation of toroidal harmonics.
Comput. Phys. Comm. 139 (2), pp. 186–191.
-
A. Gil, D. Ruiz-Antolín, J. Segura, and N. M. Temme (2016)
Algorithm 969: computation of the incomplete gamma function for negative values of the argument.
ACM Trans. Math. Softw. 43 (3), pp. 26:1–26:9.
-
A. Gil, J. Segura, and N. M. Temme (2000)
Computing toroidal functions for wide ranges of the parameters.
J. Comput. Phys. 161 (1), pp. 204–217.
-
A. Gil, J. Segura, and N. M. Temme (2001)
On nonoscillating integrals for computing inhomogeneous Airy functions.
Math. Comp. 70 (235), pp. 1183–1194.
-
A. Gil, J. Segura, and N. M. Temme (2002a)
Algorithm 819: AIZ, BIZ: two Fortran 77 routines for the computation of complex Airy functions.
ACM Trans. Math. Software 28 (3), pp. 325–336.
-
A. Gil, J. Segura, and N. M. Temme (2002b)
Algorithm 822: GIZ, HIZ: two Fortran 77 routines for the computation of complex Scorer functions.
ACM Trans. Math. Software 28 (4), pp. 436–447.
-
A. Gil, J. Segura, and N. M. Temme (2002c)
Computing complex Airy functions by numerical quadrature.
Numer. Algorithms 30 (1), pp. 11–23.
-
A. Gil, J. Segura, and N. M. Temme (2002d)
Evaluation of the modified Bessel function of the third kind of imaginary orders.
J. Comput. Phys. 175 (2), pp. 398–411.
-
A. Gil, J. Segura, and N. M. Temme (2003a)
Computation of the modified Bessel function of the third kind of imaginary orders: Uniform Airy-type asymptotic expansion.
J. Comput. Appl. Math. 153 (1-2), pp. 225–234.
-
A. Gil, J. Segura, and N. M. Temme (2003b)
Computing special functions by using quadrature rules.
Numer. Algorithms 33 (1-4), pp. 265–275.
-
A. Gil, J. Segura, and N. M. Temme (2003c)
On the zeros of the Scorer functions.
J. Approx. Theory 120 (2), pp. 253–266.
-
A. Gil, J. Segura, and N. M. Temme (2004a)
Algorithm 831: Modified Bessel functions of imaginary order and positive argument.
ACM Trans. Math. Software 30 (2), pp. 159–164.
-
A. Gil, J. Segura, and N. M. Temme (2004b)
Computing solutions of the modified Bessel differential equation for imaginary orders and positive arguments.
ACM Trans. Math. Software 30 (2), pp. 145–158.
-
A. Gil, J. Segura, and N. M. Temme (2004c)
Integral representations for computing real parabolic cylinder functions.
Numer. Math. 98 (1), pp. 105–134.
-
A. Gil, J. Segura, and N. M. Temme (2006a)
Computing the real parabolic cylinder functions
, 
.
ACM Trans. Math. Software 32 (1), pp. 70–101.
-
A. Gil, J. Segura, and N. M. Temme (2006b)
Algorithm 850: Real parabolic cylinder functions , .
ACM Trans. Math. Software 32 (1), pp. 102–112.
-
A. Gil, J. Segura, and N. M. Temme (2006c)
The ABC of hyper recursions.
J. Comput. Appl. Math. 190 (1-2), pp. 270–286.
-
A. Gil, J. Segura, and N. M. Temme (2007a)
Numerical Methods for Special Functions.
Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA.
-
A. Gil, J. Segura, and N. M. Temme (2007b)
Numerically satisfactory solutions of hypergeometric recursions.
Math. Comp. 76 (259), pp. 1449–1468.
-
A. Gil, J. Segura, and N. M. Temme (2009)
Computing the conical function
.
SIAM J. Sci. Comput. 31 (3), pp. 1716–1741.
-
A. Gil, J. Segura, and N. M. Temme (2011a)
Algorithm 914: parabolic cylinder function
and its derivative.
ACM Trans. Math. Software 38 (1), pp. Art. 6, 5.
-
A. Gil, J. Segura, and N. M. Temme (2011b)
Fast and accurate computation of the Weber parabolic cylinder function .
IMA J. Numer. Anal. 31 (3), pp. 1194–1216.
-
A. Gil, J. Segura, and N. M. Temme (2012)
An improved algorithm and a Fortran 90 module for computing the conical function
.
Comput. Phys. Commun. 183 (3), pp. 794–799.
-
A. Gil, J. Segura, and N. M. Temme (2014)
Algorithm 939: computation of the Marcum Q-function.
ACM Trans. Math. Softw. 40 (3), pp. 20:1–20:21.
-
A. Gil and J. Segura (2003)
Computing the zeros and turning points of solutions of second order homogeneous linear ODEs.
SIAM J. Numer. Anal. 41 (3), pp. 827–855.
-
A. Gil and J. Segura (2014)
On the complex zeros of Airy and Bessel functions and those of their derivatives.
Anal. Appl. (Singap.) 12 (5), pp. 537–561.
-
P. M. W. Gill and S. Chen (2003)
Radial quadrature for multi exponential integrands.
J. Comput. Chem. 24 (4), pp. 732–740.
-
GIMPS (website)
-
S. G. Gindikin (1964)
Analysis in homogeneous domains.
Uspehi Mat. Nauk 19 (4 (118)), pp. 3–92 (Russian).
-
J. N. Ginocchio (1991)
A new identity for some six-
symbols.
J. Math. Phys. 32 (6), pp. 1430–1432.
-
E. S. Ginsberg and D. Zaborowski (1975)
Algorithm 490: The Dilogarithm function of a real argument [S22].
Comm. ACM 18 (4), pp. 200–202.
-
K. Girstmair (1990a)
A theorem on the numerators of the Bernoulli numbers.
Amer. Math. Monthly 97 (2), pp. 136–138.
-
K. Girstmair (1990b)
Dirichlet convolution of cotangent numbers and relative class number formulas.
Monatsh. Math. 110 (3-4), pp. 231–256.
-
J. W. L. Glaisher (1940)
Number-Divisor Tables.
British Association Mathematical Tables, Vol. VIII, Cambridge University Press, Cambridge, England.
-
M. L. Glasser (1976)
Definite integrals of the complete elliptic integral
.
J. Res. Nat. Bur. Standards Sect. B 80B (2), pp. 313–323.
-
M. L. Glasser (1979)
A method for evaluating certain Bessel integrals.
Z. Angew. Math. Phys. 30 (4), pp. 722–723.
-
M. Goano (1995)
Algorithm 745: Computation of the complete and incomplete Fermi-Dirac integral.
ACM Trans. Math. Software 21 (3), pp. 221–232.
-
C. D. Godsil, M. Grötschel, and D. J. A. Welsh (1995)
Combinatorics in Statistical Physics.
In Handbook of Combinatorics, Vol. 2, R. L. Graham, M. Grötschel, and L. Lovász (Eds.),
pp. 1925–1954.
-
W. M. Y. Goh (1998)
Plancherel-Rotach asymptotics for the Charlier polynomials.
Constr. Approx. 14 (2), pp. 151–168.
-
D. Goldberg (1991)
What every computer scientist should know about floating-point arithmetic.
ACM Computing Surveys 23 (1), pp. 5–48.
-
K. Goldberg, F. T. Leighton, M. Newman, and S. L. Zuckerman (1976)
Tables of binomial coefficients and Stirling numbers.
J. Res. Nat. Bur. Standards Sect. B 80B (1), pp. 99–171.
-
S. Goldstein (1927)
Mathieu functions.
Trans. Camb. Philos. Soc. 23, pp. 303–336.
-
G. H. Golub and G. Meurant (2010)
Matrices, moments and quadrature with applications.
Princeton Series in Applied Mathematics, Princeton University Press, Princeton, NJ.
-
G. H. Golub and C. F. Van Loan (1996)
Matrix Computations.
3rd edition, Johns Hopkins University Press, Baltimore, MD.
-
G. H. Golub and J. H. Welsch (1969)
Calculation of Gauss quadrature rules.
Math. Comp. 23 (106), pp. 221–230.
-
V. V. Golubev (1960)
Lectures on Integration of the Equations of Motion of a Rigid Body About a Fixed Point.
Translated from the Russian by J. Shorr-Kon, Office of Technical Services, U. S. Department of Commerce, Washington, D.C..
-
D. Gómez-Ullate, N. Kamran, and R. Milson (2010)
Exceptional orthogonal polynomials and the Darboux transformation.
J. Phys. A 43 (43), pp. 43016, 16 pp..
-
D. Gómez-Ullate and R. Milson (2014)
Rational extensions of the quantum harmonic oscillator and exceptional Hermite polynomials.
J. Phys. A 47 (1), pp. 015203, 26 pp..
-
D. Gómez-Ullate, N. Kamran, and R. Milson (2009)
An extended class of orthogonal polynomials defined by a Sturm-Liouville problem.
J. Math. Anal. Appl. 359 (1), pp. 352–367.
-
Z. Gong, L. Zejda, W. Dappen, and J. M. Aparicio (2001)
Generalized Fermi-Dirac functions and derivatives: Properties and evaluation.
Comput. Phys. Comm. 136 (3), pp. 294–309.
-
E. T. Goodwin and J. Staton (1948)
Table of
.
Quart. J. Mech. Appl. Math. 1 (1), pp. 319–326.
-
E. T. Goodwin (1949a)
Recurrence relations for cross-products of Bessel functions.
Quart. J. Mech. Appl. Math. 2 (1), pp. 72–74.
-
E. T. Goodwin (1949b)
The evaluation of integrals of the form
.
Proc. Cambridge Philos. Soc. 45 (2), pp. 241–245.
-
R. G. Gordon (1968)
Error bounds in equilibrium statistical mechanics.
J. Math. Phys. 9, pp. 655–663.
-
R. G. Gordon (1969)
New method for constructing wavefunctions for bound states and scattering.
J. Chem. Phys. 51, pp. 14–25.
-
R. G. Gordon (1970)
Constructing wavefunctions for nonlocal potentials.
J. Chem. Phys. 52, pp. 6211–6217.
-
D. Goss (1978)
Von Staudt for
![{\mathbf{F}}_{q}[{T}]](.././bib/m143.png)
.
Duke Math. J. 45 (4), pp. 885–910.
-
K. Gottfried and T. Yan (2004)
Quantum mechanics: fundamentals.
Second edition, Springer-Verlag, New York.
-
D. Gottlieb and S. A. Orszag (1977)
Numerical Analysis of Spectral Methods: Theory and Applications.
Society for Industrial and Applied Mathematics, Philadelphia, PA.
-
H. P. W. Gottlieb (1985)
On the exceptional zeros of cross-products of derivatives of spherical Bessel functions.
Z. Angew. Math. Phys. 36 (3), pp. 491–494.
-
H. W. Gould (1960)
Stirling number representation problems.
Proc. Amer. Math. Soc. 11 (3), pp. 447–451.
-
H. W. Gould (1972)
Explicit formulas for Bernoulli numbers.
Amer. Math. Monthly 79, pp. 44–51.
-
É. Goursat (1883)
Mémoire sur les fonctions hypergéométriques d’ordre supérieur.
Ann. Sci. École Norm. Sup. (2) 12, pp. 261–286, 395–430 (French).
-
É. Goursat (1881)
Sur l’équation différentielle linéaire, qui admet pour intégrale la série hypergéométrique.
Ann. Sci. École Norm. Sup. (2) 10, pp. 3–142 (French).
-
J. Grad and E. Zakrajšek (1973)
Method for evaluation of zeros of Bessel functions.
J. Inst. Math. Appl. 11, pp. 57–72.
-
I. S. Gradshteyn and I. M. Ryzhik (2015)
Table of integrals, series, and products.
Eighth edition, Elsevier/Academic Press, Amsterdam.
-
R. L. Graham, M. Grötschel, and L. Lovász (Eds.) (1995)
Handbook of Combinatorics. Vols. 1, 2.
Elsevier Science B.V., Amsterdam.
-
R. L. Graham, D. E. Knuth, and O. Patashnik (1994)
Concrete Mathematics: A Foundation for Computer Science.
2nd edition, Addison-Wesley Publishing Company, Reading, MA.
-
B. Grammaticos, A. Ramani, and V. Papageorgiou (1991)
Do integrable mappings have the Painlevé property?.
Phys. Rev. Lett. 67 (14), pp. 1825–1828.
-
T. V. Gramtcheff (1981)
An application of Airy functions to the Tricomi problem.
Math. Nachr. 102 (1), pp. 169–181.
-
Ya. I. Granovskiĭ, I. M. Lutzenko, and A. S. Zhedanov (1992)
Mutual integrability, quadratic algebras, and dynamical symmetry.
Ann. Phys. 217 (1), pp. 1–20.
-
A. Gray, G. B. Mathews, and T. M. MacRobert (1922)
A Treatise on Bessel Functions and their Applications to Physics.
2nd edition, Macmillan and Co., London.
-
J. J. Gray (2000)
Linear Differential Equations and Group Theory from Riemann to Poincaré.
2nd edition, Birkhäuser Boston Inc., Boston, MA.
-
N. Gray (2002)
Automatic reduction of elliptic integrals using Carlson’s relations.
Math. Comp. 71 (237), pp. 311–318.
-
M. B. Green, J. H. Schwarz, and E. Witten (1988a)
Superstring Theory: Introduction, Vol. 1.
2nd edition, Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge.
-
M. B. Green, J. H. Schwarz, and E. Witten (1988b)
Superstring Theory: Loop Amplitudes, Anomalies and Phenomenolgy, Vol. 2.
2nd edition, Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge.
-
C. H. Greene, U. Fano, and G. Strinati (1979)
General form of the quantum-defect theory.
Phys. Rev. A 19 (4), pp. 1485–1509.
-
D. H. Greene and D. E. Knuth (1982)
Mathematics for the Analysis of Algorithms.
Progress in Computer Science, Vol. 1, Birkhäuser Boston, Boston, MA.
-
A. G. Greenhill (1892)
The Applications of Elliptic Functions.
MacMillan, London.
-
A. G. Greenhill (1959)
The Applications of Elliptic Functions.
Dover Publications Inc., New York.
-
W. Greiner, B. Müller, and J. Rafelski (1985)
Quantum Electrodynamics of Strong Fields: With an Introduction into Modern Relativistic Quantum Mechanics.
Texts and Monographs in Physics, Springer.
-
W. Gröbner and N. Hofreiter (1949)
Integraltafel. Erster Teil. Unbestimmte Integrale.
Springer-Verlag, Vienna.
-
W. Gröbner and N. Hofreiter (1950)
Integraltafel. Zweiter Teil. Bestimmte Integrale.
Springer-Verlag, Vienna and Innsbruck.
-
P. Groeneboom and D. R. Truax (2000)
A monotonicity property of the power function of multivariate tests.
Indag. Math. (N.S.) 11 (2), pp. 209–218.
-
W. Groenevelt (2007)
Fourier transforms related to a root system of rank 1.
Transform. Groups 12 (1), pp. 77–116.
-
V. I. Gromak and N. A. Lukaševič (1982)
Special classes of solutions of Painlevé equations.
Differ. Uravn. 18 (3), pp. 419–429 (Russian).
-
V. I. Gromak (1975)
Theory of Painlevé’s equations.
Differ. Uravn. 11 (11), pp. 373–376 (Russian).
-
V. I. Gromak (1976)
The solutions of Painlevé’s fifth equation.
Differ. Uravn. 12 (4), pp. 740–742 (Russian).
-
V. I. Gromak (1978)
One-parameter systems of solutions of Painlevé equations.
Differ. Uravn. 14 (12), pp. 2131–2135 (Russian).
-
V. I. Gromak (1987)
Theory of the fourth Painlevé equation.
Differ. Uravn. 23 (5), pp. 760–768, 914 (Russian).
-
V. I. Gromak, I. Laine, and S. Shimomura (2002)
Painlevé Differential Equations in the Complex Plane.
Studies in Mathematics, Vol. 28, Walter de Gruyter & Co., Berlin-New York.
-
E. P. Gross and S. Ziering (1958)
Kinetic theory of linear shear flow.
Phys. Fluids 1 (3), pp. 215–224.
-
K. I. Gross and R. A. Kunze (1976)
Bessel functions and representation theory. I.
J. Functional Analysis 22 (2), pp. 73–105.
-
K. I. Gross and D. St. P. Richards (1987)
Special functions of matrix argument. I. Algebraic induction, zonal polynomials, and hypergeometric functions.
Trans. Amer. Math. Soc. 301 (2), pp. 781–811.
-
K. I. Gross and D. St. P. Richards (1991)
Hypergeometric functions on complex matrix space.
Bull. Amer. Math. Soc. (N.S.) 24 (2), pp. 349–355.
-
E. Grosswald (1978)
Bessel Polynomials.
Lecture Notes in Mathematics, Vol. 698, Springer, Berlin-New York.
-
E. Grosswald (1985)
Representations of Integers as Sums of Squares.
Springer-Verlag, New York.
-
F. W. Grover (1946)
Inductance Calculations.
Van Nostrand, New York.
-
GSL (free C library)
GNU Scientific Library
The GNU Project.
-
X. Guan, O. Zatsarinny, K. Bartschat, B. I. Schneider, J. Feist, and C. J. Noble (2007)
General approach to few-cycle intense laser interactions with complex atoms.
Phys. Rev. A 76, pp. 053411.
-
J. H. Gunn (1967)
Algorithm 300: Coulomb wave functions.
Comm. ACM 10 (4), pp. 244–245.
-
B. Guo (1998)
Spectral Methods and Their Applications.
World Scientific Publishing Co. Inc., River Edge, NJ-Singapore.
-
B. N. Gupta (1970)
On Mill’s ratio.
Proc. Cambridge Philos. Soc. 67, pp. 363–364.
-
D. P. Gupta and M. E. Muldoon (2000)
Riccati equations and convolution formulae for functions of Rayleigh type.
J. Phys. A 33 (7), pp. 1363–1368.
-
H. Gupta, C. E. Gwyther, and J. C. P. Miller (1958)
Tables of Partitions.
Royal Society Math. Tables, Vol. 4, Cambridge University Press.
-
H. Gupta (1935)
A table of partitions.
Proc. London Math. Soc. (2) 39, pp. 142–149.
-
H. Gupta (1937)
A table of partitions (II).
Proc. London Math. Soc. (2) 42, pp. 546–549.
-
R. A. Gustafson (1987)
Multilateral summation theorems for ordinary and basic hypergeometric series in
.
SIAM J. Math. Anal. 18 (6), pp. 1576–1596.
-
A. Guthmann (1991)
Asymptotische Entwicklungen für unvollständige Gammafunktionen.
Forum Math. 3 (2), pp. 105–141 (German).
-
J. C. Gutiérrez-Vega, R. M. Rodríguez-Dagnino, M. A. Meneses-Nava, and S. Chávez-Cerda (2003)
Mathieu functions, a visual approach.
Amer. J. Phys. 71 (3), pp. 233–242.
-
A. J. Guttmann and T. Prellberg (1993)
Staircase polygons, elliptic integrals, Heun functions, and lattice Green functions.
Phys. Rev. E 47 (4), pp. R2233–R2236.
