Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8888)

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=-21/4, b_1`>=-11/2

For fixed z and a₁=-21/4, b_1`=3/2

http://functions.wolfram.com/07.22.03.8888.01

Input Form

HypergeometricPFQ[{-(21/4)}, {3/2, 7/4}, z] == (-4 z^(1/4) (299674823175 - 2166875757900 Sqrt[z] - 606464727120 z + 2788391511360 z^(3/2) + 147439756800 z^2 - 616149596160 z^(5/2) - 9411010560 z^3 + 38200049664 z^(7/2) + 188940288 z^4 - 758906880 z^(9/2) - 1048576 z^5 + 4194304 z^(11/2) + E^(4 Sqrt[z]) (-299674823175 - 2166875757900 Sqrt[z] + 606464727120 z + 2788391511360 z^(3/2) - 147439756800 z^2 - 616149596160 z^(5/2) + 9411010560 z^3 + 38200049664 z^(7/2) - 188940288 z^4 - 758906880 z^(9/2) + 1048576 z^5 + 4194304 z^(11/2))) - E^(2 Sqrt[z]) Sqrt[2 Pi] (316234143225 - 10119492583200 z + 11565134380800 z^2 - 2492150169600 z^3 + 153363087360 z^4 - 3038773248 z^5 + 16777216 z^6) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] (316234143225 - 10119492583200 z + 11565134380800 z^2 - 2492150169600 z^3 + 153363087360 z^4 - 3038773248 z^5 + 16777216 z^6) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z])/ (23816385331200 z^(3/4))

Standard Form

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MathML 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]