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h21-0003

contiguity relation

$  {}_2F_1((a+ 1 ),b,c,z)=((\frac{z}{a}\cdot
{\tt weylalgebra1.partialdiff}
( {}_2F_1(a,b,c,z),{\tt List}({\tt List}(z, 1 ))))+( 1 \cdot  {}_2F_1(a,b,c,z))) $
Typeset by om2tex.xsl

$ {}_2 F_1 (1 + a,b,c,z) = {}_2 F_1 (a,b,c,z) + {\frac{
{\tt z}
 
{\tt weylalgebra1Partialdiff}
({}_2 F_1 (a,b,c,z),\{ \{
{\tt z}
,1\} \} )}{
{\tt a}
}} $
Typeset by Mathematica

Formula in the tfb format:

(hypergeo1.hypergeometric2F1(a ~arith1.plus~ 1, b, c, z)) ~relation1.eq~ 
(((arith1.divide((z)  , (a) ) )  ~arith1.times~ 
weylalgebra1.partialdiff(hypergeo1.hypergeometric2F1(a, b, c, z), 
list1.list(list1.list(z, 1)))) ~arith1.plus~ ((1)  ~arith1.times~ 
hypergeo1.hypergeometric2F1(a, b, c, z)));

Contiguity relation of the Gauss Hypergeometric series with respect to the variable a.

Reference: [4, 60]

Proof: [3, 41-47] Retrieve the formula in Mathematica form h21-0003-math-auto.m Retrieve the formula in Risa/Asir form h21-0003-asir-auto.rr Retrieve the formula in LaTeX form h21-0003-tex-auto.tex Interactive replacement h21-0003-js-auto.html


Nobuki Takayama 2003-02-03