Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7421)

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=-19/4

http://functions.wolfram.com/07.22.03.7421.01

Input Form

HypergeometricPFQ[{5}, {-(19/4), -(1/4)}, -z] == (1/790020) (4 (197505 - 831600 z + 574875 z^2 + 312480 z^3 + 60576 z^4 - 512 z^5) - Sqrt[Pi] z^(5/4) FresnelS[(2 z^(1/4))/Sqrt[Pi]] ((4385745 - 5290740 z - 2484720 z^2 - 505344 z^3 + 4096 z^4) Cos[2 Sqrt[z]] + 42 Sqrt[z] (208845 + 26520 z - 8704 z^2 + 2048 z^3) Sin[2 Sqrt[z]]) + Sqrt[Pi] z^(5/4) FresnelC[(2 z^(1/4))/Sqrt[Pi]] (-42 Sqrt[z] (208845 + 26520 z - 8704 z^2 + 2048 z^3) Cos[2 Sqrt[z]] + (4385745 - 5290740 z - 2484720 z^2 - 505344 z^3 + 4096 z^4) 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]