Content-Length: 31376 | pFad | https://dlmf.nist.gov/./../././.././././././././././././././../././bib/../././bib/.././13.25#p2

DLMF: §13.25 Products ‣ Whittaker Functions ‣ Chapter 13 Confluent Hypergeometric Functions

About the Project

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

§13.25 Products

ⓘ

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		$M_{\kappa,\mu}\left(z\right)M_{\kappa,-\mu-1}\left(z\right)+\frac{(\frac{1}{2}% +\mu+\kappa)(\frac{1}{2}+\mu-\kappa)}{4\mu(1+\mu)(1+2\mu)^{2}}M_{\kappa,\mu+1}% \left(z\right)M_{\kappa,-\mu}\left(z\right)=1.$
ⓘ Symbols: $M_{\NVar{\kappa},\NVar{\mu}}\left(\NVar{z}\right)$ : Whittaker confluent hypergeometric function and $z$ : 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

© 2010–2024 NIST / Disclaimer / Feedback; Version 1.2.3; Release date 2024-12-15.

NIST

Site Privacy Accessibility Privacy Program Copyrights Vulnerability Disclosure No Fear Act Policy FOIA Environmental Policy Scientific Integrity Information Quality Standards Commerce.gov Science.gov USA.gov