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variants of this functions
HypergeometricPFQ




Mathematica Notation

Traditional Notation









Hypergeometric Functions > HypergeometricPFQ[{a1},{b1,b2},z] > Specific values > Specialized values > For fixed z and with symbolical integers in parameters > For fixed z and a1=m, b1=1/2-n, b2=1/2-p





http://functions.wolfram.com/07.22.03.0314.01









  


  








Input Form





HypergeometricPFQ[{1 + j}, {1/2 - m, 1/2 - n}, z] == ((-1)^(j + n)/(j! Pochhammer[1/2, n] Pochhammer[1/2, m])) Sum[Binomial[j, i] Pochhammer[1/2 - j - m, -i + j] Sum[Binomial[i + m, k] Pochhammer[-1 - n, i - k + m] ((-1)^n (1 - 2 k - 2 m - 2 n) Pochhammer[-(1/2), k + n] + (-1)^k Pi (k m + m n + z) z^((1/2) (-1 + k + n)) StruveL[-k - n, 2 Sqrt[z]] - (-1)^k m Pi z^((k + n)/2) StruveL[1 - k - n, 2 Sqrt[z]]), {k, 0, i + m}], {i, 0, j}] /; Element[j, Integers] && j >= 0 && Element[m, Integers] && m >= 0 && Element[n, Integers] && n >= 0








Standard Form





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MathML Form







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Rule Form





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Contributed by





Brychkov Yu.A. (2006)


Date Added to functions.wolfram.com (modification date)





2007-05-02