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h21-0010

contiguity relation

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

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

Formula in the tfb format:

(weylalgebra1.partialdiff(hypergeo1.hypergeometric2F1(a ~arith1.minus~ 1, b, c, 
z), list1.list(list1.list(z, 1)))) ~relation1.eq~ 
(((arith1.divide((((arith1.unary_minus(a) ~arith1.plus~ 1)  ~arith1.times~ z) 
~arith1.plus~ a ~arith1.minus~ 1)  , (a ~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.times~ a)) ~arith1.plus~ b)  , 
(a ~arith1.minus~ c) ) )  ~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 h21-0010-math-auto.m Retrieve the formula in Risa/Asir form h21-0010-asir-auto.rr Retrieve the formula in LaTeX form h21-0010-tex-auto.tex Interactive replacement h21-0010-js-auto.html


Nobuki Takayama 2003-02-03