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HypergeometricU






Mathematica Notation

Traditional Notation









Hypergeometric Functions > HypergeometricU[a,b,z] > Integration > Definite integration > Involving the direct function





http://functions.wolfram.com/07.33.21.0009.01









  


  










Input Form





Integrate[(t^(\[Alpha] - 1) HypergeometricU[a, b, t])/E^(t z), {t, 0, Infinity}] == (Pi^2 (Cot[Pi (b - \[Alpha])] + Cot[Pi \[Alpha]]) Csc[b Pi] Gamma[a - \[Alpha]] Hypergeometric2F1[\[Alpha], 1 - b + \[Alpha], 1 - a + \[Alpha], z])/(Gamma[a] Gamma[1 + a - b] Gamma[1 - \[Alpha]] Gamma[b - \[Alpha]]) - (1/Gamma[1 + a - \[Alpha]]) Pi z^(a - \[Alpha]) Csc[Pi (a - \[Alpha])] Hypergeometric2F1[a, 1 + a - b, 1 + a - \[Alpha], z] /; Re[z] > 0 && Re[\[Alpha]] > 0 && Re[1 + \[Alpha] - b] > 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)





2002-12-18





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