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

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=7/4, b_1`>=-11/2

For fixed z and a₁=7/4, b_1`=-9/2

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

Input Form

HypergeometricPFQ[{7/4}, {-(9/2), 23/4}, -z] == (1/(19327352832 z^(19/4))) (209 (5221125 Sqrt[Pi] (40897395 + 3537072 z + 155904 z^2 + 4096 z^3) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) (204 Sqrt[z] (1395623604375 - 517296780000 z + 53252908800 z^2 - 1835008000 z^3 + 16777216 z^4) Cos[2 Sqrt[z]] + (-213530411469375 + 209298277188000 z - 38960608377600 z^2 + 2316238848000 z^3 - 44040192000 z^4 + 134217728 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]