Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9562)

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/07.22.03.9562.01

Input Form

HypergeometricPFQ[{-(19/4)}, {7/2, 9/4}, z] == (4 (-36404121600 - 72808243200 Sqrt[z] + 631004774400 z - 634562826975 z^(3/2) + 4590265056300 z^2 + 1174339509840 z^(5/2) - 5288191513920 z^3 - 233243112960 z^(7/2) + 968341616640 z^4 + 12495790080 z^(9/2) - 50619383808 z^5 - 215678976 z^(11/2) + 865861632 z^6 + 1048576 z^(13/2) - 4194304 z^7 + E^(4 Sqrt[z]) (36404121600 - 72808243200 Sqrt[z] - 631004774400 z - 634562826975 z^(3/2) - 4590265056300 z^2 + 1174339509840 z^(5/2) + 5288191513920 z^3 - 233243112960 z^(7/2) - 968341616640 z^4 + 12495790080 z^(9/2) + 50619383808 z^5 - 215678976 z^(11/2) - 865861632 z^6 + 1048576 z^(13/2) + 4194304 z^7)) + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(5/4) (1993650033375 + 21265600356000 z - 21810872160000 z^2 + 3910072320000 z^3 - 203120640000 z^4 + 3466592256 z^5 - 16777216 z^6) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(5/4) (1993650033375 + 21265600356000 z - 21810872160000 z^2 + 3910072320000 z^3 - 203120640000 z^4 + 3466592256 z^5 - 16777216 z^6) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z])/ (95260586803200 z^(5/2))

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]