Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a7uh)

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`=9/2

http://functions.wolfram.com/07.22.03.a7uh.01

Input Form

HypergeometricPFQ[{-(17/4)}, {9/2, -(9/4)}, -z] == (1/(69525371520 z^(7/2))) (-2 Sqrt[z] (225881530875 - 28808079300 z + 6616209600 z^2 - 883491840 z^3 + 184074240 z^4 - 96731136 z^5 + 549453824 z^6 + 16777216 z^7) Cos[2 Sqrt[z]] - 4194304 Sqrt[Pi] z^(27/4) (527 + 16 z) FresnelS[(2 z^(1/4))/Sqrt[Pi]] - (-225881530875 + 329983453800 z + 35286451200 z^2 - 4704860160 z^3 + 743178240 z^4 - 228065280 z^5 + 268435456 z^6 + 8388608 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]