Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a7up)

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=-17/4, b_1`>=-11/2

For fixed z and a₁=-17/4, b_1`=9/2

http://functions.wolfram.com/07.22.03.a7up.01

Input Form

HypergeometricPFQ[{-(17/4)}, {9/2, -(1/4)}, -z] == (1/(4635024768 z^(7/2))) (-2 Sqrt[z] (1550674125 + 248107860 z + 400982400 z^2 - 568083456 z^3 + 4707975168 z^4 + 1127000064 z^5 + 51707904 z^6 + 524288 z^7) Cos[2 Sqrt[z]] - 512 Sqrt[Pi] z^(19/4) (38290239 + 8878896 z + 404736 z^2 + 4096 z^3) FresnelS[(2 z^(1/4))/Sqrt[Pi]] - (-1550674125 + 1819457640 z + 481178880 z^2 - 916531200 z^3 + 2004811776 z^4 + 544932864 z^5 + 25657344 z^6 + 262144 z^7) 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]