Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.6514)

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=2, b₁>=-23/4

For fixed z and a₁=2, b₁=-23/4

http://functions.wolfram.com/07.22.03.6514.01

Input Form

HypergeometricPFQ[{2}, {-(23/4), 15/4}, z] == (1/(419520 z^(11/4))) ((16 E^(2 Sqrt[z]) z^(3/4) (80405325 + 18918900 z + 1701660 z^2 + 51712 z^3 + 256 z^4) + E^(4 Sqrt[z]) Sqrt[2 Pi] (241215975 - 482431950 Sqrt[z] + 470269800 z - 297297000 z^(3/2) + 136216080 z^2 - 47567520 z^(5/2) + 12862080 z^3 - 2661120 z^(7/2) + 403200 z^4 - 40448 z^(9/2) + 2048 z^5) Erf[Sqrt[2] z^(1/4)] - Sqrt[2 Pi] (241215975 + 482431950 Sqrt[z] + 470269800 z + 297297000 z^(3/2) + 136216080 z^2 + 47567520 z^(5/2) + 12862080 z^3 + 2661120 z^(7/2) + 403200 z^4 + 40448 z^(9/2) + 2048 z^5) 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]