Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8sh)

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=-13/4, b_1`>=-11/2

For fixed z and a₁=-13/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.a8sh.01

Input Form

HypergeometricPFQ[{-(13/4)}, {11/2, 15/4}, -z] == (1/(7670731898880 z^(9/2))) (7 (Sqrt[Pi] z^(7/4) (741422907225 - 924371416800 z + 821663481600 z^2 + 922569523200 z^3 + 96268124160 z^4 + 2535456768 z^5 + 16777216 z^6) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 (4 Sqrt[z] (16982784000 + 38817792000 z - 54775190925 z^2 + 42640687440 z^3 + 56594787840 z^4 + 5987475456 z^5 + 158269440 z^6 + 1048576 z^7) Cos[2 Sqrt[z]] + (-33965568000 - 32348160000 z - 21999828825 z^2 + 14830704720 z^3 + 52570252800 z^4 + 5872066560 z^5 + 157483008 z^6 + 1048576 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]