Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.6929)

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=3, b₁>=-23/4

For fixed z and a₁=3, b₁=-11/4

http://functions.wolfram.com/07.22.03.6929.01

Input Form

HypergeometricPFQ[{3}, {-(11/4), 23/4}, -z] == (1/(65536 z^(19/4))) (285 (-4 z^(3/4) (111486375 - 24916320 z + 2217600 z^2 - 73728 z^3 + 512 z^4) - Sqrt[Pi] FresnelS[(2 z^(1/4))/Sqrt[Pi]] ((-334459125 + 648107460 z - 181787760 z^2 + 16732800 z^3 - 572672 z^4 + 4096 z^5) Cos[2 Sqrt[z]] - 2 Sqrt[z] (334459125 - 202161960 z + 31157280 z^2 - 1767168 z^3 + 32768 z^4) Sin[2 Sqrt[z]]) + Sqrt[Pi] FresnelC[(2 z^(1/4))/Sqrt[Pi]] (2 Sqrt[z] (334459125 - 202161960 z + 31157280 z^2 - 1767168 z^3 + 32768 z^4) Cos[2 Sqrt[z]] + (-334459125 + 648107460 z - 181787760 z^2 + 16732800 z^3 - 572672 z^4 + 4096 z^5) 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]