next up previous
Next: h21-0005 Up: Digital Formula Book for Previous: h21-0003


h21-0004

contiguity relation

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

$
{\tt weylalgebra1Partialdiff}
({}_2 F_1 (1 + a,b,c,z),\{ \{
{\tt z}
,1\} \...
...lgebra1Partialdiff}
({}_2 F_1 (a,b,c,z),\{ \{
{\tt z}
,1\} \} )}{-a + a z}} $
Typeset by Mathematica

Formula in the tfb format:

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

Contiguity relation of the Gauss Hypergeometric series with respect to the variable a.

Reference: [4, 60]

Proof: [3, 41-47] Retrieve the formula in Mathematica form h21-0004-math-auto.m Retrieve the formula in Risa/Asir form h21-0004-asir-auto.rr Retrieve the formula in LaTeX form h21-0004-tex-auto.tex Interactive replacement h21-0004-js-auto.html


Nobuki Takayama 2003-02-03