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h21-0006

contiguity relation

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

$
{\tt weylalgebra1Partialdiff}
({}_2 F_1 (a,1 + b,c,z),\{ \{
{\tt z}
,1\} \...
...lgebra1Partialdiff}
({}_2 F_1 (a,b,c,z),\{ \{
{\tt z}
,1\} \} )}{-b + b z}} $
Typeset by Mathematica

Formula in the tfb format:

(weylalgebra1.partialdiff(hypergeo1.hypergeometric2F1(a, b ~arith1.plus~ 1, c, 
z), list1.list(list1.list(z, 1)))) ~relation1.eq~ 
(((arith1.divide((arith1.unary_minus((a ~arith1.times~ z)) ~arith1.minus~ b 
~arith1.plus~ c ~arith1.minus~ 1)  , ((b ~arith1.times~ z) ~arith1.minus~ b) ) 
)  ~arith1.times~ weylalgebra1.partialdiff(hypergeo1.hypergeometric2F1(a, b, c, 
z), list1.list(list1.list(z, 1)))) ~arith1.plus~ 
((arith1.divide((arith1.unary_minus(a))  , (z ~arith1.minus~ 1) ) )  
~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 h21-0006-math-auto.m Retrieve the formula in Risa/Asir form h21-0006-asir-auto.rr Retrieve the formula in LaTeX form h21-0006-tex-auto.tex Interactive replacement h21-0006-js-auto.html


Nobuki Takayama 2003-02-03