Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8382)

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`=7/2

http://functions.wolfram.com/07.22.03.8382.01

Input Form

HypergeometricPFQ[{-(23/4)}, {7/2, -(19/4)}, z] == (-687809261514375 + 687809261514375 E^(4 Sqrt[z]) - 1375618523028750 Sqrt[z] - 1375618523028750 E^(4 Sqrt[z]) Sqrt[z] - 853832186707500 z + 853832186707500 E^(4 Sqrt[z]) z + 126493657290000 z^(3/2) + 126493657290000 E^(4 Sqrt[z]) z^(3/2) - 20238985166400 z^2 + 20238985166400 E^(4 Sqrt[z]) z^2 + 3519823507200 z^(5/2) + 3519823507200 E^(4 Sqrt[z]) z^(5/2) - 670442572800 z^3 + 670442572800 E^(4 Sqrt[z]) z^3 + 141145804800 z^(7/2) + 141145804800 E^(4 Sqrt[z]) z^(7/2) - 33210777600 z^4 + 33210777600 E^(4 Sqrt[z]) z^4 + 8856207360 z^(9/2) + 8856207360 E^(4 Sqrt[z]) z^(9/2) - 2724986880 z^5 + 2724986880 E^(4 Sqrt[z]) z^5 + 990904320 z^(11/2) + 990904320 E^(4 Sqrt[z]) z^(11/2) - 440401920 z^6 + 440401920 E^(4 Sqrt[z]) z^6 + 251658240 z^(13/2) + 251658240 E^(4 Sqrt[z]) z^(13/2) - 201326592 z^7 + 201326592 E^(4 Sqrt[z]) z^7 + 268435456 z^(15/2) + 268435456 E^(4 Sqrt[z]) z^(15/2) - 1073741824 z^8 + 1073741824 E^(4 Sqrt[z]) z^8 - 1073741824 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(33/4) Erf[Sqrt[2] z^(1/4)] - 1073741824 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(33/4) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z])/(1403529623496000 z^(5/2))

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]