Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a7th)

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`=7/2

http://functions.wolfram.com/07.22.03.a7th.01

Input Form

HypergeometricPFQ[{-(17/4)}, {7/2, 3/4}, -z] == (1/(1046618496 z^(5/2))) (Sqrt[Pi] z^(11/4) (1760115825 + 1501965504 z + 210802176 z^2 + 7520256 z^3 + 65536 z^4) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 (4 Sqrt[z] (-1879605 - 3580200 z + 96743808 z^2 + 91584891 z^3 + 13088688 z^4 + 469248 z^5 + 4096 z^6) Cos[2 Sqrt[z]] + (3759210 + 2148120 z + 57283200 z^2 + 83121039 z^3 + 12749616 z^4 + 466176 z^5 + 4096 z^6) 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]