Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9514)

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`=5/2

http://functions.wolfram.com/07.22.03.9514.01

Input Form

HypergeometricPFQ[{-(19/4)}, {5/2, 9/4}, z] == (4 (97077657600 - 149577449175 Sqrt[z] + 1353805922700 z + 505101214800 z^(3/2) - 2350195041600 z^2 - 135293437440 z^(5/2) + 566428907520 z^3 + 9021726720 z^(7/2) - 36633477120 z^4 - 185794560 z^(9/2) + 746323968 z^5 + 1048576 z^(11/2) - 4194304 z^6 + E^(4 Sqrt[z]) (-97077657600 - 149577449175 Sqrt[z] - 1353805922700 z + 505101214800 z^(3/2) + 2350195041600 z^2 - 135293437440 z^(5/2) - 566428907520 z^3 + 9021726720 z^(7/2) + 36633477120 z^4 - 185794560 z^(9/2) - 746323968 z^5 + 1048576 z^(11/2) + 4194304 z^6)) + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(1/4) (343732764375 + 6599669076000 z - 9777287520000 z^2 + 2292111360000 z^3 - 147087360000 z^4 + 2988441600 z^5 - 16777216 z^6) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(1/4) (343732764375 + 6599669076000 z - 9777287520000 z^2 + 2292111360000 z^3 - 147087360000 z^4 + 2988441600 z^5 - 16777216 z^6) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z])/(32848478208000 z^(3/2))

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]