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# h21-0300

Connection formula of solutions between 0 and infty.

Typeset by om2tex.xsl

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]

Nobuki Takayama 2003-02-03