Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9590)

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=-19/4, b_1`>=-11/2

For fixed z and a₁=-19/4, b_1`=9/2

http://functions.wolfram.com/07.22.03.9590.01

Input Form

HypergeometricPFQ[{-(19/4)}, {9/2, -(11/4)}, z] == (1/(2814094483200 z^(7/2))) ((5155991465625 - 5155991465625 E^(4 Sqrt[z]) + 10311982931250 Sqrt[z] + 10311982931250 E^(4 Sqrt[z]) Sqrt[z] + 7589619437400 z - 7589619437400 E^(4 Sqrt[z]) z + 1429928299800 z^(3/2) + 1429928299800 E^(4 Sqrt[z]) z^(3/2) - 754247894400 z^2 + 754247894400 E^(4 Sqrt[z]) z^2 + 251415964800 z^(5/2) + 251415964800 E^(4 Sqrt[z]) z^(5/2) - 78875596800 z^3 + 78875596800 E^(4 Sqrt[z]) z^3 + 25738352640 z^(7/2) + 25738352640 E^(4 Sqrt[z]) z^(7/2) - 9196830720 z^4 + 9196830720 E^(4 Sqrt[z]) z^4 + 3746856960 z^(9/2) + 3746856960 E^(4 Sqrt[z]) z^(9/2) - 1816657920 z^5 + 1816657920 E^(4 Sqrt[z]) z^5 + 1108869120 z^(11/2) + 1108869120 E^(4 Sqrt[z]) z^(11/2) - 931135488 z^6 + 931135488 E^(4 Sqrt[z]) z^6 + 1283457024 z^(13/2) + 1283457024 E^(4 Sqrt[z]) z^(13/2) - 5234491392 z^7 + 5234491392 E^(4 Sqrt[z]) z^7 - 33554432 z^(15/2) - 33554432 E^(4 Sqrt[z]) z^(15/2) + 134217728 z^8 - 134217728 E^(4 Sqrt[z]) z^8 + 8388608 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(29/4) (-627 + 16 z) Erf[Sqrt[2] z^(1/4)] + 8388608 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(29/4) (-627 + 16 z) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z]))

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)

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]