Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a7rt)

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`=5/2

http://functions.wolfram.com/07.22.03.a7rt.01

Input Form

HypergeometricPFQ[{-(17/4)}, {5/2, -(9/4)}, -z] == (1/(181704600 z^(3/2))) (-2 Sqrt[z] (34459425 - 8149680 z + 1962240 z^2 - 1093632 z^3 + 6356992 z^4 + 262144 z^5) Cos[2 Sqrt[z]] - 65536 Sqrt[Pi] z^(19/4) (391 + 16 z) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + (34459425 + 36756720 z - 7499520 z^2 + 2519040 z^3 - 3080192 z^4 - 131072 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]