Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.6961)

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=-7/4

http://functions.wolfram.com/07.22.03.6961.01

Input Form

HypergeometricPFQ[{3}, {-(7/4), 23/4}, -z] == (1/(131072 z^(19/4))) (3135 (4 z^(3/4) (-7432425 + 1589940 z - 131040 z^2 + 3392 z^3) + Sqrt[Pi] FresnelC[(2 z^(1/4))/Sqrt[Pi]] (2 Sqrt[z] (22297275 - 13264020 z + 1945440 z^2 - 96576 z^3 + 1024 z^4) Cos[2 Sqrt[z]] + (-22297275 + 42993720 z - 11702880 z^2 + 994560 z^3 - 26624 z^4) Sin[2 Sqrt[z]]) + Sqrt[Pi] FresnelS[(2 z^(1/4))/Sqrt[Pi]] ((22297275 - 42993720 z + 11702880 z^2 - 994560 z^3 + 26624 z^4) Cos[2 Sqrt[z]] + 2 Sqrt[z] (22297275 - 13264020 z + 1945440 z^2 - 96576 z^3 + 1024 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]