Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9174)

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/07.22.03.9174.01

Input Form

HypergeometricPFQ[{-(19/4)}, {-(9/2), 5/4}, z] == (1/(29727129600 z^(1/4))) ((-4 z^(1/4) (618356025 - 1652786100 Sqrt[z] + 136704960 z - 477550080 z^(3/2) + 16657920 z^2 - 62269440 z^(5/2) + 1228800 z^3 - 4718592 z^(7/2) + 65536 z^4 - 262144 z^(9/2) + E^(4 Sqrt[z]) (618356025 + 1652786100 Sqrt[z] + 136704960 z + 477550080 z^(3/2) + 16657920 z^2 + 62269440 z^(5/2) + 1228800 z^3 + 4718592 z^(7/2) + 65536 z^4 + 262144 z^(9/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] (4334247225 + 6083154000 z + 1853913600 z^2 + 245145600 z^3 + 18677760 z^4 + 1048576 z^5) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] (4334247225 + 6083154000 z + 1853913600 z^2 + 245145600 z^3 + 18677760 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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</apply> </annotation-xml> </semantics> </math>

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]