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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/07.33.03.0046.01









  


  










Input Form





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