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h21-0002

contiguity relation

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

$
{\tt weylalgebra1Partialdiff}
({}_2 F_1 (a,b,c,z),\{ \{
{\tt z}
,1\} \} ) = {\frac{a b {}_2 F_1 (1 + a,1 + b,1 + c,z)}{c}} $
Typeset by Mathematica

Formula in the tfb format:

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

Contiguity relation of the Gauss Hypergeometric series containing a differentiation.

Reference: [4, 60]

Proof: [3, 41-47] Retrieve the formula in Mathematica form h21-0002-math-auto.m Retrieve the formula in Risa/Asir form h21-0002-asir-auto.rr Retrieve the formula in LaTeX form h21-0002-tex-auto.tex Interactive replacement h21-0002-js-auto.html


Nobuki Takayama 2003-02-03