Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.6911)

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=-13/4

http://functions.wolfram.com/07.22.03.6911.01

Input Form

HypergeometricPFQ[{3}, {-(13/4), 21/4}, -z] == -((1/(16384 z^(17/4))) (17 (2 z^(1/4) (237161925 - 82702620 z + 12806640 z^2 - 766080 z^3 + 15616 z^4) + Sqrt[Pi] FresnelC[(2 z^(1/4))/Sqrt[Pi]] ((-237161925 + 462161700 z - 133887600 z^2 + 13184640 z^3 - 503040 z^4 + 4096 z^5) Cos[2 Sqrt[z]] - 30 Sqrt[z] (15810795 - 9729720 z + 1574496 z^2 - 97536 z^3 + 2048 z^4) Sin[2 Sqrt[z]]) + Sqrt[Pi] FresnelS[(2 z^(1/4))/Sqrt[Pi]] (30 Sqrt[z] (15810795 - 9729720 z + 1574496 z^2 - 97536 z^3 + 2048 z^4) Cos[2 Sqrt[z]] + (-237161925 + 462161700 z - 133887600 z^2 + 13184640 z^3 - 503040 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]