html, body, form { margin: 0; padding: 0; width: 100%; } #calculate { position: relative; width: 177px; height: 110px; background: transparent url(/images/alphabox/embed_functions_inside.gif) no-repeat scroll 0 0; } #i { position: relative; left: 18px; top: 44px; width: 133px; border: 0 none; outline: 0; font-size: 11px; } #eq { width: 9px; height: 10px; background: transparent; position: absolute; top: 47px; right: 18px; cursor: pointer; }

 HypergeometricPFQ

 http://functions.wolfram.com/07.28.21.0004.01

 Input Form

 Integrate[(t^(\[Alpha] - 1) HypergeometricPFQ[{Subscript[a, 1], Subscript[a, 2], Subscript[a, 3], Subscript[a, 4]}, {Subscript[b, 1], Subscript[b, 2], Subscript[b, 3]}, -t])/E^(c t), {t, 0, Infinity}] == (Gamma[\[Alpha]] Gamma[-\[Alpha] + Subscript[a, 1]] Gamma[-\[Alpha] + Subscript[a, 2]] Gamma[-\[Alpha] + Subscript[a, 3]] Gamma[-\[Alpha] + Subscript[a, 4]] Gamma[Subscript[b, 1]] Gamma[Subscript[b, 2]] Gamma[Subscript[b, 3]] HypergeometricPFQ[{\[Alpha], 1 + \[Alpha] - Subscript[b, 1], 1 + \[Alpha] - Subscript[b, 2], 1 + \[Alpha] - Subscript[b, 3]}, {1 + \[Alpha] - Subscript[a, 1], 1 + \[Alpha] - Subscript[a, 2], 1 + \[Alpha] - Subscript[a, 3], 1 + \[Alpha] - Subscript[a, 4]}, c])/ (Gamma[Subscript[a, 1]] Gamma[Subscript[a, 2]] Gamma[Subscript[a, 3]] Gamma[Subscript[a, 4]] Gamma[-\[Alpha] + Subscript[b, 1]] Gamma[-\[Alpha] + Subscript[b, 2]] Gamma[-\[Alpha] + Subscript[b, 3]]) + (c^(-\[Alpha] + Subscript[a, 1]) Gamma[\[Alpha] - Subscript[a, 1]] Gamma[-Subscript[a, 1] + Subscript[a, 2]] Gamma[-Subscript[a, 1] + Subscript[a, 3]] Gamma[-Subscript[a, 1] + Subscript[a, 4]] Gamma[Subscript[b, 1]] Gamma[Subscript[b, 2]] Gamma[Subscript[b, 3]] HypergeometricPFQ[{Subscript[a, 1], 1 + Subscript[a, 1] - Subscript[b, 1], 1 + Subscript[a, 1] - Subscript[b, 2], 1 + Subscript[a, 1] - Subscript[b, 3]}, {1 - \[Alpha] + Subscript[a, 1], 1 + Subscript[a, 1] - Subscript[a, 2], 1 + Subscript[a, 1] - Subscript[a, 3], 1 + Subscript[a, 1] - Subscript[a, 4]}, c])/(Gamma[Subscript[a, 2]] Gamma[Subscript[a, 3]] Gamma[Subscript[a, 4]] Gamma[-Subscript[a, 1] + Subscript[b, 1]] Gamma[-Subscript[a, 1] + Subscript[b, 2]] Gamma[-Subscript[a, 1] + Subscript[b, 3]]) + (c^(-\[Alpha] + Subscript[a, 2]) Gamma[\[Alpha] - Subscript[a, 2]] Gamma[Subscript[a, 1] - Subscript[a, 2]] Gamma[-Subscript[a, 2] + Subscript[a, 3]] Gamma[-Subscript[a, 2] + Subscript[a, 4]] Gamma[Subscript[b, 1]] Gamma[Subscript[b, 2]] Gamma[Subscript[b, 3]] HypergeometricPFQ[{Subscript[a, 2], 1 + Subscript[a, 2] - Subscript[b, 1], 1 + Subscript[a, 2] - Subscript[b, 2], 1 + Subscript[a, 2] - Subscript[b, 3]}, {1 - \[Alpha] + Subscript[a, 2], 1 - Subscript[a, 1] + Subscript[a, 2], 1 + Subscript[a, 2] - Subscript[a, 3], 1 + Subscript[a, 2] - Subscript[a, 4]}, c])/(Gamma[Subscript[a, 1]] Gamma[Subscript[a, 3]] Gamma[Subscript[a, 4]] Gamma[-Subscript[a, 2] + Subscript[b, 1]] Gamma[-Subscript[a, 2] + Subscript[b, 2]] Gamma[-Subscript[a, 2] + Subscript[b, 3]]) + (c^(-\[Alpha] + Subscript[a, 3]) Gamma[\[Alpha] - Subscript[a, 3]] Gamma[Subscript[a, 1] - Subscript[a, 3]] Gamma[Subscript[a, 2] - Subscript[a, 3]] Gamma[-Subscript[a, 3] + Subscript[a, 4]] Gamma[Subscript[b, 1]] Gamma[Subscript[b, 2]] Gamma[Subscript[b, 3]] HypergeometricPFQ[{Subscript[a, 3], 1 + Subscript[a, 3] - Subscript[b, 1], 1 + Subscript[a, 3] - Subscript[b, 2], 1 + Subscript[a, 3] - Subscript[b, 3]}, {1 - \[Alpha] + Subscript[a, 3], 1 - Subscript[a, 1] + Subscript[a, 3], 1 - Subscript[a, 2] + Subscript[a, 3], 1 + Subscript[a, 3] - Subscript[a, 4]}, c])/(Gamma[Subscript[a, 1]] Gamma[Subscript[a, 2]] Gamma[Subscript[a, 4]] Gamma[-Subscript[a, 3] + Subscript[b, 1]] Gamma[-Subscript[a, 3] + Subscript[b, 2]] Gamma[-Subscript[a, 3] + Subscript[b, 3]]) + (c^(-\[Alpha] + Subscript[a, 4]) Gamma[\[Alpha] - Subscript[a, 4]] Gamma[Subscript[a, 1] - Subscript[a, 4]] Gamma[Subscript[a, 2] - Subscript[a, 4]] Gamma[Subscript[a, 3] - Subscript[a, 4]] Gamma[Subscript[b, 1]] Gamma[Subscript[b, 2]] Gamma[Subscript[b, 3]] HypergeometricPFQ[{Subscript[a, 4], 1 + Subscript[a, 4] - Subscript[b, 1], 1 + Subscript[a, 4] - Subscript[b, 2], 1 + Subscript[a, 4] - Subscript[b, 3]}, {1 - \[Alpha] + Subscript[a, 4], 1 - Subscript[a, 1] + Subscript[a, 4], 1 - Subscript[a, 2] + Subscript[a, 4], 1 - Subscript[a, 3] + Subscript[a, 4]}, c])/(Gamma[Subscript[a, 1]] Gamma[Subscript[a, 2]] Gamma[Subscript[a, 3]] Gamma[-Subscript[a, 4] + Subscript[b, 1]] Gamma[-Subscript[a, 4] + Subscript[b, 2]] Gamma[-Subscript[a, 4] + Subscript[b, 3]]) /; Re[\[Alpha]] > 0 && Re[c] > 0

 Standard Form

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 MathML Form

 Rule Form

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

 2001-10-29