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

§13.25 Products

Notes:: For (13.25.1) combine (13.12.1) with (13.14.4).
Keywords:: Whittaker functions
Permalink:: http://dlmf.nist.gov/13.25

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

Symbols:: $\mathop{M_{{\kappa,\mu}}\/}\nolimits\!\left(z\right)$ : Whittaker confluent hypergeometric function and : complex variable
Referenced by:: §13.25
Permalink:: http://dlmf.nist.gov/13.25.E1
Encodings:: TeX, pMML, png

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

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