Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a7za)

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=-15/4, b_1`>=-11/2

For fixed z and a₁=-15/4, b_1`=-9/2

http://functions.wolfram.com/07.22.03.a7za.01

Input Form

HypergeometricPFQ[{-(15/4)}, {-(9/2), 21/4}, z] == (221 (-4 z^(1/4) (29972021024570625 + 39962694699427500 Sqrt[z] + 23538466328454000 z + 7026407859240000 z^(3/2) + 817984685548800 z^2 + 69704791833600 z^(5/2) + 28374990336000 z^3 - 91668274790400 z^(7/2) + 5306478428160 z^4 - 19889183784960 z^(9/2) + 387223388160 z^5 - 1503091752960 z^(11/2) + 14344519680 z^6 - 56572772352 z^(13/2) + 268435456 z^7 - 1073741824 z^(15/2) + E^(4 Sqrt[z]) (29972021024570625 - 39962694699427500 Sqrt[z] + 23538466328454000 z - 7026407859240000 z^(3/2) + 817984685548800 z^2 - 69704791833600 z^(5/2) + 28374990336000 z^3 + 91668274790400 z^(7/2) + 5306478428160 z^4 + 19889183784960 z^(9/2) + 387223388160 z^5 + 1503091752960 z^(11/2) + 14344519680 z^6 + 56572772352 z^(13/2) + 268435456 z^7 + 1073741824 z^(15/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] (29972021024570625 - 8431689431088000 z + 1692382108032000 z^2 - 401157240422400 z^3 + 348832382976000 z^4 + 78334289510400 z^5 + 5968326819840 z^6 + 225485783040 z^7 + 4294967296 z^8) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] (29972021024570625 - 8431689431088000 z + 1692382108032000 z^2 - 401157240422400 z^3 + 348832382976000 z^4 + 78334289510400 z^5 + 5968326819840 z^6 + 225485783040 z^7 + 4294967296 z^8) Erfi[Sqrt[2] z^(1/4)]))/E^(2 Sqrt[z])/(310326161823498240 z^(17/4))

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]