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

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=19/4, b_1`>=-11/2

For fixed z and a₁=19/4, b_1`=-11/2

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

Input Form

HypergeometricPFQ[{19/4}, {-(11/2), 23/4}, -z] == -((1/(348798320640 z^(19/4))) (19 (26264240610733125 Sqrt[Pi] FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) (4 Sqrt[z] (8754746870244375 - 4002169997826000 z + 646815353184000 z^2 - 53072028979200 z^3 + 2626660270080 z^4 - 82842746880 z^5 + 1191182336 z^6) Cos[2 Sqrt[z]] + (-26264240610733125 + 28015189984782000 z - 7114968885024000 z^2 + 796080434688000 z^3 - 49950144921600 z^4 + 1984655523840 z^5 - 46254784512 z^6 + 268435456 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]