Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.6765)

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=2, b₁>=-23/4

For fixed z and a₁=2, b₁=11/4

http://functions.wolfram.com/07.22.03.6765.01

Input Form

HypergeometricPFQ[{2}, {11/4, 21/4}, -z] == (1/(131072 z^(17/4))) (4641 (2 z^(1/4) (1755 + 108 z + 256 z^2) - 45 Sqrt[Pi] FresnelS[(2 z^(1/4))/Sqrt[Pi]] (2 Sqrt[z] (-39 + 8 z) Cos[2 Sqrt[z]] + 3 (13 - 20 z) Sin[2 Sqrt[z]]) + 45 Sqrt[Pi] FresnelC[(2 z^(1/4))/Sqrt[Pi]] ((-39 + 60 z) Cos[2 Sqrt[z]] + 2 Sqrt[z] (-39 + 8 z) 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]