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h21-0300

Connection formula of solutions between 0 and infty.

$ ((
{\tt set1.notin}
((a1-a2),
{\tt set1.map}
(fns1.lambdax(
{\tt set1.in}
(...
...(a2-b1)+ 1 )),{\tt List}(((a2-a1)+ 1 )),\frac{ 1 }{z}))\cdot ((-z))^{(-a2)}))) $
Typeset by om2tex.xsl

$
{\tt implies}
(
{\tt logic1And}
(
{\tt set1Notin}
(
{\tt a1}
-
{\tt a2...
...}^{
{\tt a2}
}} \Gamma (
{\tt a1}
) \Gamma (-
{\tt a2}
+
{\tt b1}
)}}) $
Typeset by Mathematica

Formula in the tfb format:

logic1.implies((set1.notin(a1 - a2, set1.map(OMLBIND(OMBVAR(x), 
logic1.and(set1.in(x, setname1.Z), relation1.leq(x, 0)))))) ~logic1.and~ 
(set1.notin(b1, set1.map(OMLBIND(OMBVAR(x), logic1.and(set1.in(x, setname1.Z), 
relation1.leq(x, 0)))))), (hypergeo1.hypergeometric_pFq(list1.list(a1, a2), 
list1.list(b1), z)) ~relation1.eq~ (((((arith1.divide(((hypergeo0.gamma(b1) * 
hypergeo0.gamma(a2 - a1)))  , ((hypergeo0.gamma(b1 - a1) * 
hypergeo0.gamma(a2))) ) )  * hypergeo1.hypergeometric_pFq(list1.list(a1, (a1 - 
b1)  + 1), list1.list((a1 - a2)  + 1), arith1.divide(1 , z) )) * 
(arith1.power((arith1.unary_minus(z))  , (arith1.unary_minus((a1) )) ) ) ) + 
(((arith1.divide(((hypergeo0.gamma(b1) * hypergeo0.gamma(a1 - a2)))  , 
((hypergeo0.gamma(b1 - a2) * hypergeo0.gamma(a1))) ) )  * 
hypergeo1.hypergeometric_pFq(list1.list(a2, (a2 - b1)  + 1), list1.list((a2 - 
a1)  + 1), arith1.divide(1 , z) )) * (arith1.power((arith1.unary_minus(z))  , 
(arith1.unary_minus((a2) )) ) ) )) ));

Connection formula of 2F1 between 0 and infty for generaic values of parameters.

Reference: [0]

Proof: [0] Retrieve the formula in Mathematica form h21-0300-math-auto.m Retrieve the formula in Risa/Asir form h21-0300-asir-auto.rr Retrieve the formula in LaTeX form h21-0300-tex-auto.tex Interactive replacement h21-0300-js-auto.html


Nobuki Takayama 2003-02-03