Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a99w)

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=-9/4, b_1`>=-11/2

For fixed z and a₁=-9/4, b_1`=-11/2

http://functions.wolfram.com/07.22.03.a99w.01

Input Form

HypergeometricPFQ[{-(9/4)}, {-(11/2), 19/4}, z] == (4 z^(1/4) (42706082293875 + 56941443058500 Sqrt[z] + 35479975330800 z + 12599468481600 z^(3/2) + 2568604147200 z^2 + 392784537600 z^(5/2) - 1535385600 z^3 + 51934691328 z^(7/2) - 794886144 z^4 + 3138650112 z^(9/2) - 13631488 z^5 + 54525952 z^(11/2) + E^(4 Sqrt[z]) (-42706082293875 + 56941443058500 Sqrt[z] - 35479975330800 z + 12599468481600 z^(3/2) - 2568604147200 z^2 + 392784537600 z^(5/2) + 1535385600 z^3 + 51934691328 z^(7/2) + 794886144 z^4 + 3138650112 z^(9/2) + 13631488 z^5 + 54525952 z^(11/2))) + 13 E^(2 Sqrt[z]) Sqrt[2 Pi] (-3285083253375 + 774859932000 z - 134174880000 z^2 + 32901120000 z^3 + 15792537600 z^4 + 962592768 z^5 + 16777216 z^6) Erf[Sqrt[2] z^(1/4)] - 13 E^(2 Sqrt[z]) Sqrt[2 Pi] (-3285083253375 + 774859932000 z - 134174880000 z^2 + 32901120000 z^3 + 15792537600 z^4 + 962592768 z^5 + 16777216 z^6) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z])/ (1649267441664 z^(15/4))

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]