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HypergeometricU






Mathematica Notation

Traditional Notation









Hypergeometric Functions > HypergeometricU[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/07.33.03.0048.01









  


  










Input Form





HypergeometricU[1/2 - n, -m, z] == (((-1)^n n! z)/(Sqrt[Pi] Pochhammer[3/2, m])) E^(z/2) Sum[(((-1)^k (k + m)!)/k!) LaguerreL[-k + n, -(1/2) + k, z] Sum[(-1)^p Sum[(((-1)^j z^j)/(2^(2 j) j!)) LaguerreL[-j + p, 1 + j - p, -(z/2)] Sum[Binomial[j, i] (BesselK[-1 - 2 i + j, z/2] - BesselK[-2 i + j, z/2]), {i, 0, j}], {j, 0, p}], {p, 0, 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