next up previous
Next: h21-0014 Up: Digital Formula Book for Previous: h21-0012


h21-0013

contiguity relation

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

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

Formula in the tfb format:

(hypergeo1.hypergeometric2F1(a, b, c ~arith1.minus~ 1, z)) ~relation1.eq~ 
(((arith1.divide((z)  , (c ~arith1.minus~ 1) ) )  ~arith1.times~ 
weylalgebra1.partialdiff(hypergeo1.hypergeometric2F1(a, b, c, z), 
list1.list(list1.list(z, 1)))) ~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 h21-0013-math-auto.m Retrieve the formula in Risa/Asir form h21-0013-asir-auto.rr Retrieve the formula in LaTeX form h21-0013-tex-auto.tex Interactive replacement h21-0013-js-auto.html


Nobuki Takayama 2003-02-03