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variants of this functions
HypergeometricPFQ






Mathematica Notation

Traditional Notation









Hypergeometric Functions > HypergeometricPFQ[{a1,a2,a3,a4,a5},{b1,b2,b3,b4},z] > Specific values > Values at z=1 > For fixed a2, a3





http://functions.wolfram.com/07.29.03.0007.01









  


  










Input Form





HypergeometricPFQ[{1, b, c, b + 1/2, c + 1/2}, {1/2 - b + n, 1 - b + n, 1/2 - c + n, 1 - c + n}, 1] == 1 - ((1 + (-1)^n) Pochhammer[2 b - 2 n, n] Pochhammer[2 c - 2 n, n])/ (4 Pochhammer[1 - 2 b, n] Pochhammer[1 - 2 c, n]) + Gamma[1 - 2 b] Gamma[1 - 2 c] (((Sqrt[Pi] Gamma[1/2 - 2 b - 2 c + 2 n] Pochhammer[1 - 4 b + 2 n, 2 n] Pochhammer[1 - 4 c + 2 n, 2 n])/(2^(4 n) Gamma[1/2 - 2 b + 2 n] Gamma[1/2 - 2 c + 2 n]) + (-1)^n Pochhammer[1 - 2 b + n, n] Pochhammer[1 - 2 c + n, n])/(4 Gamma[1 - 2 b - 2 c + 2 n])) - Sum[(Pochhammer[2 b - 2 n, 2 k] Pochhammer[2 c - 2 n, 2 k])/ (Pochhammer[1 - 2 b, 2 k] Pochhammer[1 - 2 c, 2 k]), {k, 0, Floor[(n - 1)/2]}] /; Re[b + c] < n + 1/4 && Element[n, Integers] && n > 0










Standard Form





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MathML Form







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Rule Form





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





2001-10-29





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