13 Confluent Hypergeometric Functions Kummer Functions 13.11 Series 13.13 Addition and Multiplication Theorems

§13.12 Products

Notes:: (13.12.1) follows from the fact that its left-hand side is bounded at infinity: use (13.2.39)–(13.2.41), and (13.7.3).
Keywords:: Kummer functions
Permalink:: http://dlmf.nist.gov/13.12

13.12.1 $\mathop{M\/}\nolimits\!\left(a,b,z\right)\mathop{M\/}\nolimits\!\left(-a,-b,-z% \right)+\frac{a(a-b)z^{2}}{b^{2}(1-b^{2})}\mathop{M\/}\nolimits\!\left(1+a,2+b% ,z\right)\mathop{M\/}\nolimits\!\left(1-a,2-b,-z\right)=1.$

Symbols:: $\mathop{M\/}\nolimits\!\left(a,b,z\right)$ : Kummer confluent hypergeometric function and : complex variable
Referenced by:: §13.12, §13.25
Permalink:: http://dlmf.nist.gov/13.12.E1
Encodings:: TeX, pMML, png

For generalizations of this quadratic relation see Majima et al. (2000).

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

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