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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 Bessel I





http://functions.wolfram.com/07.18.26.0119.01









  


  








Input Form





Hypergeometric0F1Regularized[b, z] BesselI[-b - n, 2 Sqrt[z]] == (1/Sqrt[Pi]) (Sum[(((-1)^Floor[(1 + n)/2] Gamma[1/2 + k - n + Floor[n/2]])/ (k! Gamma[b + k] Gamma[1 - b + k - n])) Pochhammer[1 - k + Floor[n/2], n - Floor[n/2]] (4 z)^k, {k, 0, Floor[n/2]}]/(2^n z^((b + n)/2)) - (-1)^Floor[n/2] 2^(b - 1/2) Pi MeijerG[{{(1 - b)/2, 1 - b/2}, {(3 - 2 b)/4}}, {{1 + (n - b)/2}, {(b + n)/2, -((b + n)/2), 1 - (3 b + n)/2, (3 - 2 b)/4}}, 4 z]) /; Element[n, Integers] && n >= 0








Standard Form





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MathML Form







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<apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <ci> b </ci> <ci> n </ci> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> b </ci> </apply> <ci> n </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 4 </cn> <apply> <plus /> <cn type='integer'> 3 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> </apply> </apply> </apply> </apply> </list> </list> <apply> <times /> <cn type='integer'> 4 </cn> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <in /> <ci> n </ci> <integers /> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2007-05-02