Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a97y)

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

For fixed z and a₁=-11/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.a97y.01

Input Form

HypergeometricPFQ[{-(11/4)}, {11/2, -(3/4)}, z] == (1/(492211200 z^(9/2))) ((-5065535475 + 5065535475 E^(4 Sqrt[z]) - 10131070950 Sqrt[z] - 10131070950 E^(4 Sqrt[z]) Sqrt[z] - 8132424300 z + 8132424300 E^(4 Sqrt[z]) z - 2756754000 z^(3/2) - 2756754000 E^(4 Sqrt[z]) z^(3/2) + 32432400 z^2 - 32432400 E^(4 Sqrt[z]) z^2 + 138378240 z^(5/2) + 138378240 E^(4 Sqrt[z]) z^(5/2) - 82494720 z^3 + 82494720 E^(4 Sqrt[z]) z^3 + 42577920 z^(7/2) + 42577920 E^(4 Sqrt[z]) z^(7/2) - 23654400 z^4 + 23654400 E^(4 Sqrt[z]) z^4 + 15728640 z^(9/2) + 15728640 E^(4 Sqrt[z]) z^(9/2) - 13959168 z^5 + 13959168 E^(4 Sqrt[z]) z^5 + 19922944 z^(11/2) + 19922944 E^(4 Sqrt[z]) z^(11/2) - 82837504 z^6 + 82837504 E^(4 Sqrt[z]) z^6 - 1048576 z^(13/2) - 1048576 E^(4 Sqrt[z]) z^(13/2) + 4194304 z^7 - 4194304 E^(4 Sqrt[z]) z^7 + 262144 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(25/4) (-319 + 16 z) Erf[Sqrt[2] z^(1/4)] + 262144 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(25/4) (-319 + 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]