13 Confluent Hypergeometric Functions Whittaker Functions 13.24 Series 13.26 Addition and Multiplication Theorems

§13.25 Products

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Keywords:: Whittaker functions, products
Notes:: For (13.25.1) combine (13.12.1) with (13.14.4).
Permalink:: http://dlmf.nist.gov/13.25
See also:: Annotations for Ch.13

13.25.1 $M_{\kappa,\mu}\left(z\right)M_{\kappa,-\mu-1}\left(z\right)+\frac{(\frac{1}{2}% +\mu+\kappa)(\frac{1}{2}+\mu-\kappa)}{4\mu(1+\mu)(1+2\mu)^{2}}M_{\kappa,\mu+1}% \left(z\right)M_{\kappa,-\mu}\left(z\right)=1.$

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Symbols:: $M_{\NVar{\kappa},\NVar{\mu}}\left(\NVar{z}\right)$ : Whittaker confluent hypergeometric function and : complex variable
Referenced by:: §13.25
Permalink:: http://dlmf.nist.gov/13.25.E1
Encodings:: TeX, pMML, png
See also:: Annotations for §13.25 and Ch.13

For integral representations, integrals, and series containing products of $M_{\kappa,\mu}\left(z\right)$ and $W_{\kappa,\mu}\left(z\right)$ see Erdélyi et al. (1953a, §6.15.3).

13.24 Series 13.26 Addition and Multiplication Theorems

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