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h21-0014

contiguity relation

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

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

Formula in the tfb format:

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

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

Reference: [4, 60]

Proof: [3, 41-47] Retrieve the formula in Mathematica form h21-0014-math-auto.m Retrieve the formula in Risa/Asir form h21-0014-asir-auto.rr Retrieve the formula in LaTeX form h21-0014-tex-auto.tex Interactive replacement h21-0014-js-auto.html


Nobuki Takayama 2003-02-03