Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9230)

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=-19/4, b_1`>=-11/2

For fixed z and a₁=-19/4, b_1`=-7/2

http://functions.wolfram.com/07.22.03.9230.01

Input Form

HypergeometricPFQ[{-(19/4)}, {-(7/2), 13/4}, z] == (1/(6313601925120 z^(9/4))) ((4 z^(1/4) (-498438430875 - 664584574500 Sqrt[z] - 46231970400 z + 343437494400 z^(3/2) - 54392244480 z^2 + 190032675840 z^(5/2) - 10502553600 z^3 + 38693437440 z^(7/2) - 1245511680 z^4 + 4783865856 z^(9/2) - 123731968 z^5 + 545259520 z^(11/2) + 16777216 z^6 - 67108864 z^(13/2) + E^(4 Sqrt[z]) (-498438430875 + 664584574500 Sqrt[z] - 46231970400 z - 343437494400 z^(3/2) - 54392244480 z^2 - 190032675840 z^(5/2) - 10502553600 z^3 - 38693437440 z^(7/2) - 1245511680 z^4 - 4783865856 z^(9/2) - 123731968 z^5 - 545259520 z^(11/2) + 16777216 z^6 + 67108864 z^(13/2))) - E^(2 Sqrt[z]) Sqrt[2 Pi] (-498438430875 + 485435689200 z - 1226363846400 z^2 - 726734131200 z^3 - 151009689600 z^4 - 18827182080 z^5 - 2231369728 z^6 + 268435456 z^7) Erf[Sqrt[2] z^(1/4)] - E^(2 Sqrt[z]) Sqrt[2 Pi] (-498438430875 + 485435689200 z - 1226363846400 z^2 - 726734131200 z^3 - 151009689600 z^4 - 18827182080 z^5 - 2231369728 z^6 + 268435456 z^7) Erfi[Sqrt[2] z^(1/4)])/E^(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]