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h21-0008

contiguity relation

$
{\tt weylalgebra1.partialdiff}
( {}_2F_1(a,b,(c+ 1 ),z),{\tt List}({\tt Lis...
...)}{(((((b-c)\cdot a)-(c\cdot b))+(c)^{ 2 })\cdot z)}\cdot  {}_2F_1(a,b,c,z))) $
Typeset by om2tex.xsl

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

Formula in the tfb format:

(weylalgebra1.partialdiff(hypergeo1.hypergeometric2F1(a, b, c ~arith1.plus~ 1, 
z), list1.list(list1.list(z, 1)))) ~relation1.eq~ 
(((arith1.divide(((arith1.power(c , 2)  ~arith1.times~ z) ~arith1.minus~ 
arith1.power(c , 2) )  , (((((b ~arith1.minus~ c)  ~arith1.times~ a) 
~arith1.minus~ (c ~arith1.times~ b) ~arith1.plus~ arith1.power(c , 2) )  
~arith1.times~ z)) ) )  ~arith1.times~ 
weylalgebra1.partialdiff(hypergeo1.hypergeometric2F1(a, b, c, z), 
list1.list(list1.list(z, 1)))) ~arith1.plus~ ((arith1.divide((((c 
~arith1.times~ b) ~arith1.times~ a))  , (((((b ~arith1.minus~ c)  
~arith1.times~ a) ~arith1.minus~ (c ~arith1.times~ b) ~arith1.plus~ 
arith1.power(c , 2) )  ~arith1.times~ z)) ) )  ~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 h21-0008-math-auto.m Retrieve the formula in Risa/Asir form h21-0008-asir-auto.rr Retrieve the formula in LaTeX form h21-0008-tex-auto.tex Interactive replacement h21-0008-js-auto.html


Nobuki Takayama 2003-02-03