Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.aa7d)

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=-5/4, b_1`>=-11/2

For fixed z and a₁=-5/4, b_1`=-9/2

http://functions.wolfram.com/07.22.03.aa7d.01

Input Form

HypergeometricPFQ[{-(5/4)}, {-(9/2), 23/4}, -z] == -((209 (13 Sqrt[Pi] (5475138755625 + 947051028000 z + 104358240000 z^2 + 10967040000 z^3 + 1754726400 z^4 - 534773760 z^5 + 16777216 z^6) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) (4 Sqrt[z] (23725601274375 - 6742101366000 z + 329043187200 z^2 + 170598400 z^3 - 437059584 z^4 + 13631488 z^5) Cos[2 Sqrt[z]] + (-71176803823125 + 63610260714000 z - 7505974694400 z^2 + 126705868800 z^3 - 447283200 z^4 + 13631488 z^5) Sin[2 Sqrt[z]])))/(3298534883328 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]