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h21-0012

contiguity relation

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

$
{\tt weylalgebra1Partialdiff}
({}_2 F_1 (a,-1 + b,c,z),\{ \{
{\tt z}
,1\} ...
...eylalgebra1Partialdiff}
({}_2 F_1 (a,b,c,z),\{ \{
{\tt z}
,1\} \} )}{b - c}} $
Typeset by Mathematica

Formula in the tfb format:

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

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

Reference: [4, 60]

Proof: [3, 41-47] Retrieve the formula in Mathematica form h21-0012-math-auto.m Retrieve the formula in Risa/Asir form h21-0012-asir-auto.rr Retrieve the formula in LaTeX form h21-0012-tex-auto.tex Interactive replacement h21-0012-js-auto.html


Nobuki Takayama 2003-02-03