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h21-0011

contiguity relation

$  {}_2F_1(a,(b- 1 ),c,z)=((\frac{((-(z)^{ 2 })+z)}{((-b)+c)}\cdot
{\tt weyla...
...t}(z, 1 ))))+(\frac{(((-(a\cdot z))-b)+c)}{((-b)+c)}\cdot  {}_2F_1(a,b,c,z))) $
Typeset by om2tex.xsl

$ {}_2 F_1 (a,-1 + b,c,z) = {\frac{\left( -
{\tt b}
+
{\tt c}
-
{\tt a}
\...
...iff}
({}_2 F_1 (a,b,c,z),\{ \{
{\tt z}
,1\} \} )}{-
{\tt b}
+
{\tt c}
}} $
Typeset by Mathematica

Formula in the tfb format:

(hypergeo1.hypergeometric2F1(a, b ~arith1.minus~ 1, c, z)) ~relation1.eq~ 
(((arith1.divide((arith1.unary_minus(arith1.power(z , 2) ) ~arith1.plus~ z)  , 
(arith1.unary_minus(b) ~arith1.plus~ c) ) )  ~arith1.times~ 
weylalgebra1.partialdiff(hypergeo1.hypergeometric2F1(a, b, c, z), 
list1.list(list1.list(z, 1)))) ~arith1.plus~ 
((arith1.divide((arith1.unary_minus((a ~arith1.times~ z)) ~arith1.minus~ b 
~arith1.plus~ c)  , (arith1.unary_minus(b) ~arith1.plus~ 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 h21-0011-math-auto.m Retrieve the formula in Risa/Asir form h21-0011-asir-auto.rr Retrieve the formula in LaTeX form h21-0011-tex-auto.tex Interactive replacement h21-0011-js-auto.html


Nobuki Takayama 2003-02-03