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hpq-0210

Edited by Hiromasa Nakayama

$ (\frac{( 2 )^{y}}{(\Gamma(((\frac{ 1 }{ 2 }+\frac{t}{ 2 })+\frac{x}{ 2 }))\cdo...
...{\tt List}(( 2 \cdot y),((\frac{ 1 }{ 2 }+\frac{t}{ 2 })+\frac{y}{ 2 })), 1 )) $
Typeset by om2tex.xsl

$ {\frac{{2^y}  {}_pF_q(\{ x,{\frac{1}{2}} + x,t - y\} ,\{ {\frac{1}{2}} + {\f...
... {\frac{t}{2}} + {\frac{y}{2}}) \Gamma ({\frac{-t}{2}} + x + {\frac{y}{2}})}} $
Typeset by Mathematica

Formula in the tfb format:

    (arith1.power(2, y) 
     / 
     (hypergeo0.gamma(1 / 2 + (t / 2) + (x / 2)) *
      hypergeo0.gamma(x / 2 + y - (t / 2))) 
     *
     hypergeo1.hypergeometric_pFq(
      list1.list(t - y, x, x + (1 / 2)),
      list1.list(2 * x, 1 / 2 + (t / 2) + (x / 2)), 1))
    =
    (arith1.power(2, x)
     / 
     (hypergeo0.gamma(1 / 2 + (t / 2) + (y / 2)) *
      hypergeo0.gamma(y / 2 + x - (t / 2))) 
     *
     hypergeo1.hypergeometric_pFq(
      list1.list(t - x, y, y + (1 / 2)),
      list1.list(2 * y, 1 / 2 + (t / 2) + (y / 2)), 1));

Some identities involving hypergeometric series of lower orders

Reference: Retrieve the formula in Mathematica form hpq-0210-math-auto.m Retrieve the formula in Risa/Asir form hpq-0210-asir-auto.rr Retrieve the formula in LaTeX form hpq-0210-tex-auto.tex Interactive replacement hpq-0210-js-auto.html


Nobuki Takayama 2003-02-03