Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8306)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For rational parameters with larger denominators and fixed z

For fixed z and a₁=-23/4, b_1`>=-11/2

For fixed z and a₁=-23/4, b_1`=3/2

http://functions.wolfram.com/07.22.03.8306.01

Input Form

HypergeometricPFQ[{-(23/4)}, {3/2, 1/4}, z] == (1/(160392960000 Sqrt[z])) ((-4 (2907273600 - 14234572800 Sqrt[z] + 111079987200 z + 34868419425 z^(3/2) - 161151398100 z^2 - 8851227840 z^(5/2) + 37020318720 z^3 + 576529920 z^(7/2) - 2340587520 z^4 - 11714560 z^(9/2) + 47054848 z^5 + 65536 z^(11/2) - 262144 z^6 + E^(4 Sqrt[z]) (-2907273600 - 14234572800 Sqrt[z] - 111079987200 z + 34868419425 z^(3/2) + 161151398100 z^2 - 8851227840 z^(5/2) - 37020318720 z^3 + 576529920 z^(7/2) + 2340587520 z^4 - 11714560 z^(9/2) - 47054848 z^5 + 65536 z^(11/2) + 262144 z^6)) + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(5/4) (-527056905375 + 669278610000 z - 149768640000 z^2 + 9397248000 z^3 - 188416000 z^4 + 1048576 z^5) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(5/4) (-527056905375 + 669278610000 z - 149768640000 z^2 + 9397248000 z^3 - 188416000 z^4 + 1048576 z^5) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z]))

Standard Form

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MathML Form

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

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]