Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8qw)

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=-13/4, b_1`>=-11/2

For fixed z and a₁=-13/4, b_1`=9/2

http://functions.wolfram.com/07.22.03.a8qw.01

Input Form

HypergeometricPFQ[{-(13/4)}, {9/2, 7/4}, z] == (1/(1594847232 z^(7/2))) ((-4 (2211300 + 4422600 Sqrt[z] + 1010880 z - 3875040 z^(3/2) + 3369600 z^2 + 13478400 z^(5/2) + 22262175 z^3 - 105755436 z^(7/2) - 6653232 z^4 + 27637440 z^(9/2) + 355584 z^5 - 1434624 z^(11/2) - 4096 z^6 + 16384 z^(13/2) + E^(4 Sqrt[z]) (-2211300 + 4422600 Sqrt[z] - 1010880 z - 3875040 z^(3/2) - 3369600 z^2 + 13478400 z^(5/2) - 22262175 z^3 - 105755436 z^(7/2) + 6653232 z^4 + 27637440 z^(9/2) - 355584 z^5 - 1434624 z^(11/2) + 4096 z^6 + 16384 z^(13/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(11/4) (-103536225 + 441754560 z - 111601152 z^2 + 5750784 z^3 - 65536 z^4) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(11/4) (103536225 - 441754560 z + 111601152 z^2 - 5750784 z^3 + 65536 z^4) 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]