Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.6517)

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=-23/4

http://functions.wolfram.com/07.22.03.6517.01

Input Form

HypergeometricPFQ[{2}, {-(23/4), 19/4}, -z] == (1/(55936 z^(15/4))) (4 z^(3/4) (2400673275 - 525096000 z + 45405360 z^2 - 1453664 z^3 + 13056 z^4) + Sqrt[Pi] FresnelC[(2 z^(1/4))/Sqrt[Pi]] (2 Sqrt[z] (-7202019825 + 4318914600 z - 650810160 z^2 + 35418240 z^3 - 661760 z^4 + 2048 z^5) Cos[2 Sqrt[z]] + (7202019825 - 13921607700 z + 3848644800 z^2 - 343062720 z^3 + 11278080 z^4 - 103424 z^5) Sin[2 Sqrt[z]]) + Sqrt[Pi] FresnelS[(2 z^(1/4))/Sqrt[Pi]] ((-7202019825 + 13921607700 z - 3848644800 z^2 + 343062720 z^3 - 11278080 z^4 + 103424 z^5) Cos[2 Sqrt[z]] + 2 Sqrt[z] (-7202019825 + 4318914600 z - 650810160 z^2 + 35418240 z^3 - 661760 z^4 + 2048 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]