List of Tables
-
15 Hypergeometric Function
- 15.8.1 Quadratic transformations of the hypergeometric function.
-
18 Orthogonal Polynomials
- 18.3.1 Orthogonality properties for classical OP’s.
- 18.5.1 Classical OP’s: Rodrigues formulas (18.5.5).
- 18.6.1 Classical OP’s: symmetry and special values.
- 18.8.1 Classical OP’s: differential equations
.
- 18.9.1 Classical OP’s: recurrence relations (18.9.1).
- 18.9.2 Classical OP’s: recurrence relations (18.9.2_1).
- 18.10.1 Classical OP’s: contour integral representations (18.10.8).
- 18.19.1 Orthogonality properties for Hahn, Krawtchouk, Meixner, and Charlier OP’s.
- 18.19.2 Hahn, Krawtchouk, Meixner, and Charlier OP’s: leading coefficients.
- 18.20.1 Krawtchouk, Meixner, and Charlier OP’s: Rodrigues formulas
(18.20.1).
- 18.22.1 Recurrence relations (18.22.2) for Krawtchouk,
Meixner, and Charlier polynomials.
- 18.22.2 Difference equations (18.22.12) for Krawtchouk,
Meixner, and Charlier polynomials.
- 18.25.1 Wilson class OP’s: transformations of variable, orthogonality ranges,
and parameter constraints.
- 18.25.2 Wilson class OP’s: leading coefficients.
- 18.39.1 Typical Non-Classical Weight Functions Of Use In DVR Applicationsa
-
22 Jacobian Elliptic Functions
- 22.4.1 Periods and poles of Jacobian elliptic functions.
- 22.4.2 Periods and zeros of Jacobian elliptic functions.
- 22.4.3 Half- or quarter-period shifts of variable for the Jacobian elliptic
functions.
- 22.5.1 Jacobian elliptic function values
- 22.5.2 Other special values of Jacobian elliptic functions.
- 22.5.3 Limiting forms of Jacobian elliptic functions as
.
- 22.5.4 Limiting forms of Jacobian elliptic functions as
.
- 22.6.1 Jacobi’s imaginary transformation of Jacobian elliptic functions.
- 22.13.1 Derivatives of Jacobian elliptic functions with respect to variable.
-
24 Bernoulli and Euler Polynomials
- 24.2.1 Bernoulli and Euler numbers.
- 24.2.2 Bernoulli and Euler polynomials.
- 24.2.3 Bernoulli numbers
.
- 24.2.4 Euler numbers
.
- 24.2.5 Coefficients
of the Bernoulli polynomials.
- 24.2.6 Coefficients
of the Euler polynomials.
- 24.15.1 Genocchi and Tangent numbers.
-
26 Combinatorial Analysis
- 26.2.1 Partitions
.
- 26.3.1 Binomial coefficients
.
- 26.3.2 Binomial coefficients
for lattice paths.
- 26.4.1 Multinomials and partitions.
- 26.5.1 Catalan numbers.
- 26.6.1 Delannoy numbers
.
- 26.6.2 Motzkin numbers
.
- 26.6.3 Narayana numbers
.
- 26.6.4 Schröder numbers
.
- 26.7.1 Bell numbers.
- 26.8.1 Stirling numbers of the first kind
.
- 26.8.2 Stirling numbers of the second kind
.
- 26.9.1 Partitions
.
- 26.10.1 Partitions restricted by difference conditions.
- 26.12.1 Plane partitions.
- 26.14.1 Eulerian numbers
.
- 26.17.1 The twelvefold way.
-
27 Functions of Number Theory
- 27.2.1 Primes.
- 27.2.2 Functions related to division.
-
28 Mathieu Functions and Hill’s Equation
- 28.1.1 Notations for parameters in Mathieu’s equation.
- 28.2.1 Eigenvalues of Mathieu’s equation.
- 28.2.2 Eigenfunctions of Mathieu’s equation.
- 28.6.1 Radii of convergence for power-series expansions
of eigenvalues of Mathieu’s equation.
-
29 Lamé Functions
- 29.3.1 Eigenvalues of Lamé’s equation.
- 29.3.2 Lamé functions.
- 29.12.1 Lamé polynomials.
-
36 Integrals with Coalescing Saddles
- 36.6.1 Special cases of scaling exponents for cuspoids.
- 36.7.1 Zeros of cusp diffraction catastrophe to 5D.
and orthonormal versions 
of the classical orthogonal polynomials.
.
.
computed by Olver’s algorithm.
.
.
.
.
, 
for the minimax rational approximation 
.
.
.
.
of 
.
of 
.
.
and 
.
and 
.