Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a9i1)

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=-9/4, b_1`>=-11/2

For fixed z and a₁=-9/4, b_1`=1/2

http://functions.wolfram.com/07.22.03.a9i1.01

Input Form

HypergeometricPFQ[{-(9/4)}, {1/2, 23/4}, -z] == (209 (Sqrt[Pi] (-32564156625 - 14302688400 z - 4800902400 z^2 - 2032128000 z^3 - 2167603200 z^4 + 20808990720 z^5 + 7398752256 z^6 + 268435456 z^7) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) (4 Sqrt[z] (-10854718875 + 194594400 z - 222808320 z^2 - 232243200 z^3 + 1220739072 z^4 + 459276288 z^5 + 16777216 z^6) Cos[2 Sqrt[z]] + (32564156625 - 20432412000 z - 1633685760 z^2 - 201277440 z^3 + 928972800 z^4 + 446693376 z^5 + 16777216 z^6) Sin[2 Sqrt[z]])))/(2886218022912 z^(19/4))

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]