Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7109)

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=4, b₁>=-23/4

For fixed z and a₁=4, b₁=-21/4

http://functions.wolfram.com/07.22.03.7109.01

Input Form

HypergeometricPFQ[{4}, {-(21/4), -(3/4)}, -z] == (1/1879605) (1879605 - 1909440 z + 6040800 z^2 - 132480 z^3 - 236032 z^4 + 8192 z^5 - 16 Sqrt[Pi] z^(7/4) FresnelC[(2 z^(1/4))/Sqrt[Pi]] ((-(-329175 + 461700 z + 103056 z^2 + 14080 z^3)) Cos[2 Sqrt[z]] + 2 Sqrt[z] (329175 - 22800 z - 16416 z^2 + 512 z^3) Sin[2 Sqrt[z]]) + 16 Sqrt[Pi] z^(7/4) FresnelS[(2 z^(1/4))/Sqrt[Pi]] (2 Sqrt[z] (329175 - 22800 z - 16416 z^2 + 512 z^3) Cos[2 Sqrt[z]] + (-329175 + 461700 z + 103056 z^2 + 14080 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]