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h21-0007

contiguity relation

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

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

Formula in the tfb format:

(hypergeo1.hypergeometric2F1(a, b, c ~arith1.plus~ 1, z)) ~relation1.eq~ 
(((arith1.divide((arith1.unary_minus((c ~arith1.times~ z)) ~arith1.plus~ c)  , 
(((b ~arith1.minus~ c)  ~arith1.times~ a) ~arith1.minus~ (c ~arith1.times~ b) 
~arith1.plus~ arith1.power(c , 2) ) ) )  ~arith1.times~ 
weylalgebra1.partialdiff(hypergeo1.hypergeometric2F1(a, b, c, z), 
list1.list(list1.list(z, 1)))) ~arith1.plus~ 
((arith1.divide((arith1.unary_minus((c ~arith1.times~ a)) ~arith1.minus~ (c 
~arith1.times~ b) ~arith1.plus~ 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~ 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 h21-0007-math-auto.m Retrieve the formula in Risa/Asir form h21-0007-asir-auto.rr Retrieve the formula in LaTeX form h21-0007-tex-auto.tex Interactive replacement h21-0007-js-auto.html


Nobuki Takayama 2003-02-03