Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.aaoj)

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=-3/4, b_1`>=-11/2

For fixed z and a₁=-3/4, b_1`=-7/2

http://functions.wolfram.com/07.22.03.aaoj.01

Input Form

HypergeometricPFQ[{-(3/4)}, {-(7/2), 17/4}, -z] == (1/(1879048192 z^(13/4))) (39 (-77 Sqrt[Pi] (-23892975 - 6292800 z - 1313280 z^2 - 737280 z^3 + 65536 z^4) FresnelC[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) (-11 (167250825 - 134351280 z + 7514880 z^2 + 28672 z^3) Cos[2 Sqrt[z]] + 4 Sqrt[z] (-613253025 + 118829040 z - 5180160 z^2 + 315392 z^3) 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]