Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9638)

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`=11/2

http://functions.wolfram.com/07.22.03.9638.01

Input Form

HypergeometricPFQ[{-(19/4)}, {11/2, -(11/4)}, z] == (-1046666267521875 + 1046666267521875 E^(4 Sqrt[z]) - 2093332535043750 Sqrt[z] - 2093332535043750 E^(4 Sqrt[z]) Sqrt[z] - 1711789166587500 z + 1711789166587500 E^(4 Sqrt[z]) z - 632468286450000 z^(3/2) - 632468286450000 E^(4 Sqrt[z]) z^(3/2) - 35418224041200 z^2 + 35418224041200 E^(4 Sqrt[z]) z^2 + 28158588057600 z^(5/2) + 28158588057600 E^(4 Sqrt[z]) z^(5/2) - 9218585376000 z^3 + 9218585376000 E^(4 Sqrt[z]) z^3 + 2681770291200 z^(7/2) + 2681770291200 E^(4 Sqrt[z]) z^(7/2) - 788755968000 z^4 + 788755968000 E^(4 Sqrt[z]) z^4 + 247973806080 z^(9/2) + 247973806080 E^(4 Sqrt[z]) z^(9/2) - 86518333440 z^5 + 86518333440 E^(4 Sqrt[z]) z^5 + 34681651200 z^(11/2) + 34681651200 E^(4 Sqrt[z]) z^(11/2) - 16625172480 z^6 + 16625172480 E^(4 Sqrt[z]) z^6 + 10066329600 z^(13/2) + 10066329600 E^(4 Sqrt[z]) z^(13/2) - 8405385216 z^7 + 8405385216 E^(4 Sqrt[z]) z^7 + 11542724608 z^(15/2) + 11542724608 E^(4 Sqrt[z]) z^(15/2) - 46976204800 z^8 + 46976204800 E^(4 Sqrt[z]) z^8 - 268435456 z^(17/2) - 268435456 E^(4 Sqrt[z]) z^(17/2) + 1073741824 z^9 - 1073741824 E^(4 Sqrt[z]) z^9 + 67108864 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(33/4) (-703 + 16 z) Erf[Sqrt[2] z^(1/4)] + 67108864 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(33/4) (-703 + 16 z) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z])/ (46276220390400 z^(9/2))

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]