Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8486)

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=-23/4, b_1`>=-11/2

For fixed z and a₁=-23/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.8486.01

Input Form

HypergeometricPFQ[{-(23/4)}, {11/2, -(11/4)}, z] == (-24073324153003125 + 24073324153003125 E^(4 Sqrt[z]) - 48146648306006250 Sqrt[z] - 48146648306006250 E^(4 Sqrt[z]) Sqrt[z] - 38422448401837500 z + 38422448401837500 E^(4 Sqrt[z]) z - 12649365729000000 z^(3/2) - 12649365729000000 E^(4 Sqrt[z]) z^(3/2) + 521153868034800 z^2 - 521153868034800 E^(4 Sqrt[z]) z^2 + 789320421489600 z^(5/2) + 789320421489600 E^(4 Sqrt[z]) z^(5/2) - 408634748121600 z^3 + 408634748121600 E^(4 Sqrt[z]) z^3 + 154201791744000 z^(7/2) + 154201791744000 E^(4 Sqrt[z]) z^(7/2) - 54424161792000 z^4 + 54424161792000 E^(4 Sqrt[z]) z^4 + 19631997665280 z^(9/2) + 19631997665280 E^(4 Sqrt[z]) z^(9/2) - 7624513290240 z^5 + 7624513290240 E^(4 Sqrt[z]) z^5 + 3326465802240 z^(11/2) + 3326465802240 E^(4 Sqrt[z]) z^(11/2) - 1704905932800 z^6 + 1704905932800 E^(4 Sqrt[z]) z^6 + 1087478169600 z^(13/2) + 1087478169600 E^(4 Sqrt[z]) z^(13/2) - 944322379776 z^7 + 944322379776 E^(4 Sqrt[z]) z^7 + 1332916256768 z^(15/2) + 1332916256768 E^(4 Sqrt[z]) z^(15/2) - 5514469572608 z^8 + 5514469572608 E^(4 Sqrt[z]) z^8 - 62780342272 z^(17/2) - 62780342272 E^(4 Sqrt[z]) z^(17/2) + 252731981824 z^9 - 252731981824 E^(4 Sqrt[z]) z^9 + 536870912 z^(19/2) + 536870912 E^(4 Sqrt[z]) z^(19/2) - 2147483648 z^10 + 2147483648 E^(4 Sqrt[z]) z^10 - 8388608 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(33/4) (662929 - 30176 z + 256 z^2) Erf[Sqrt[2] z^(1/4)] - 8388608 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(33/4) (662929 - 30176 z + 256 z^2) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z])/(1897325036006400 z^(9/2))

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]