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variants of this functions
Hypergeometric1F1




Mathematica Notation

Traditional Notation









Hypergeometric Functions > Hypergeometric1F1[a,b,z] > Specific values > Specialized values > For fixed z and with symbolical integers in parameters > For fixed z and a=1/2+-n, b=m





http://functions.wolfram.com/07.20.03.0120.01









  


  








Input Form





Hypergeometric1F1[1/2 + n, m, z] == ((2^(1 - m) E^(z/2) (-1 + m)! n!)/(Pochhammer[1/2, -1 + m] Pochhammer[1/2, n])) Sum[((-z)^k/(2^k k!)) LaguerreL[-k + n, -(1/2) + k, -z] Sum[((-1)^p Binomial[-1 + k + m, p] Sum[Binomial[p, j] BesselI[p - 2 j, z/2], {j, 0, p}])/2^p, {p, 0, -1 + k + m}], {k, 0, n}] /; Element[n, Integers] && n >= 0 && Element[m, Integers] && m > 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