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variants of this functions
Hypergeometric0F1Regularized




Mathematica Notation

Traditional Notation









Hypergeometric Functions > Hypergeometric0F1Regularized[b,z] > Representations through more general functions > Through Meijer G > Classical cases involving 0F1





http://functions.wolfram.com/07.18.26.0158.01









  


  








Input Form





Hypergeometric0F1Regularized[1 - b - n, z] Hypergeometric0F1[b, z] == (Gamma[b]/(2^(n + 1) Sqrt[Pi])) (2 Sum[(((-1)^Floor[(n + 1)/2] Gamma[1/2 - n + Floor[n/2] + k])/ (k! Gamma[b + k] Gamma[1 - b - n + k])) Pochhammer[1 - k + Floor[n/2], n - Floor[n/2]] (4 z)^k, {k, 0, Floor[n/2]}] - (-1)^n Pi MeijerG[{{(1 + n)/2, (2 + n)/2}, {1/2}}, {{1 + n}, {b + n, 0, 1 - b, 1/2}}, 4 z]) /; 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)





2007-05-02