Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7391)

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=5, b₁>=-23/4

For fixed z and a₁=5, b₁=-21/4

http://functions.wolfram.com/07.22.03.7391.01

Input Form

HypergeometricPFQ[{5}, {-(21/4), -(19/4)}, -z] == (1/41247931725) (41247931725 - 8270262000 z + 1556755200 z^2 - 406425600 z^3 + 206438400 z^4 - 396361728 z^5 - 1210245120 z^6 + 18743296 z^7 - 4096 Sqrt[Pi] z^(23/4) FresnelC[(2 z^(1/4))/Sqrt[Pi]] ((1142505 - 117024 z + 256 z^2) Cos[2 Sqrt[z]] + 96 Sqrt[z] (-6443 + 96 z) Sin[2 Sqrt[z]]) - 4096 Sqrt[Pi] z^(23/4) FresnelS[(2 z^(1/4))/Sqrt[Pi]] (-96 Sqrt[z] (-6443 + 96 z) Cos[2 Sqrt[z]] + (1142505 - 117024 z + 256 z^2) Sin[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]