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h21-0001

Contiguity relation

Edited by Nobuki Takayama

$ ((((a\cdot ( 1 -z))\cdot  {}_2F_1((a+ 1 ),b,c,z))+(((c-( 2 \cdot a))+((a-b)\cdot z))\cdot  {}_2F_1(a,b,c,z)))+((a-c)\cdot  {}_2F_1((a- 1 ),b,c,z)))= 0 $
Typeset by om2tex.xsl

$ \left( a - c \right)  {}_2 F_1 (-1 + a,b,c,z) + \left( -2 a + c + \left( a -...
...t)  {}_2 F_1 (a,b,c,z) + a \left( 1 - z \right)  {}_2 F_1 (1 + a,b,c,z) = 0 $
Typeset by Mathematica

Formula in the tfb format:

      (
        ((a*(1-z))*hypergeo1.hypergeometric2F1(a+1,b,c,z))
       +
        ((c-(2*a)+((a-b)*z))*hypergeo1.hypergeometric2F1(a,b,c,z))
       +
        ((a-c)*hypergeo1.hypergeometric2F1(a-1,b,c,z))
      ) = 0 ;

Contiguity relation of the Gauss Hypergeometric series with respect to the variable a. A paper on an algorithmic method to derive contiguity relations can be found here http://www.math.kobe-u.ac.jp/ taka/jsiam1989.pdf .

Reference: [4, 60]

Proof: [3, 41-47] Retrieve the formula in Mathematica form h21-0001-math-auto.m Retrieve the formula in Risa/Asir form h21-0001-asir-auto.rr Retrieve the formula in LaTeX form h21-0001-tex-auto.tex Interactive replacement h21-0001-js-auto.html


Nobuki Takayama 2003-02-03