Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8494)

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/07.22.03.8494.01

Input Form

HypergeometricPFQ[{-(23/4)}, {11/2, -(3/4)}, z] == (-99613755115875 + 99613755115875 E^(4 Sqrt[z]) - 199227510231750 Sqrt[z] - 199227510231750 E^(4 Sqrt[z]) Sqrt[z] - 143660653636500 z + 143660653636500 E^(4 Sqrt[z]) z - 21684626964000 z^(3/2) - 21684626964000 E^(4 Sqrt[z]) z^(3/2) + 20536617301200 z^2 - 20536617301200 E^(4 Sqrt[z]) z^2 - 850377528000 z^(5/2) - 850377528000 E^(4 Sqrt[z]) z^(5/2) - 6541365600000 z^3 + 6541365600000 E^(4 Sqrt[z]) z^3 + 7326329472000 z^(7/2) + 7326329472000 E^(4 Sqrt[z]) z^(7/2) - 6512292864000 z^4 + 6512292864000 E^(4 Sqrt[z]) z^4 + 6008547409920 z^(9/2) + 6008547409920 E^(4 Sqrt[z]) z^(9/2) - 6738308628480 z^5 + 6738308628480 E^(4 Sqrt[z]) z^5 + 11299116810240 z^(11/2) + 11299116810240 E^(4 Sqrt[z]) z^(11/2) - 51774703534080 z^6 + 51774703534080 E^(4 Sqrt[z]) z^6 - 2573035960320 z^(13/2) - 2573035960320 E^(4 Sqrt[z]) z^(13/2) + 10658220957696 z^7 - 10658220957696 E^(4 Sqrt[z]) z^7 + 128514097152 z^(15/2) + 128514097152 E^(4 Sqrt[z]) z^(15/2) - 519879131136 z^8 + 519879131136 E^(4 Sqrt[z]) z^8 - 1969750016 z^(17/2) - 1969750016 E^(4 Sqrt[z]) z^(17/2) + 7904165888 z^9 - 7904165888 E^(4 Sqrt[z]) z^9 + 8388608 z^(19/2) + 8388608 E^(4 Sqrt[z]) z^(19/2) - 33554432 z^10 + 33554432 E^(4 Sqrt[z]) z^10 - 512 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(25/4) (104679803745 - 21001590720 z + 1018258944 z^2 - 15450112 z^3 + 65536 z^4) Erf[Sqrt[2] z^(1/4)] - 512 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(25/4) (104679803745 - 21001590720 z + 1018258944 z^2 - 15450112 z^3 + 65536 z^4) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z])/(73921754649600 z^(9/2))

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]