Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8cj)

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=-15/4, b_1`>=-11/2

For fixed z and a₁=-15/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.a8cj.01

Input Form

HypergeometricPFQ[{-(15/4)}, {11/2, 17/4}, -z] == (Sqrt[Pi] z^(5/4) (-155819489450625 + 215454108870000 z - 159104572704000 z^2 + 249575800320000 z^3 + 63384330240000 z^4 + 3477083258880 z^5 + 58133053440 z^6 + 268435456 z^7) FresnelC[(2 z^(1/4))/Sqrt[Pi]] - 2 ((-Sqrt[z]) (-15021490176000 + 24202623146625 z - 15423327612000 z^2 + 12575721312000 z^3 + 3770643824640 z^4 + 213973401600 z^5 + 3617587200 z^6 + 16777216 z^7) Cos[2 Sqrt[z]] + 4 (-1877686272000 - 13948526592000 z + 16443715936725 z^2 - 11693525104800 z^3 + 14936134752000 z^4 + 3922221219840 z^5 + 216643338240 z^6 + 3630170112 z^7 + 16777216 z^8) Sin[2 Sqrt[z]]))/ (191063968972800 z^(9/2))

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]