Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8390)

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/07.22.03.8390.01

Input Form

HypergeometricPFQ[{-(23/4)}, {7/2, -(11/4)}, z] == (1/(4924665345600 z^(5/2))) ((-948702429675 + 948702429675 E^(4 Sqrt[z]) - 1897404859350 Sqrt[z] - 1897404859350 E^(4 Sqrt[z]) Sqrt[z] - 903526123500 z + 903526123500 E^(4 Sqrt[z]) z + 722820898800 z^(3/2) + 722820898800 E^(4 Sqrt[z]) z^(3/2) - 340151011200 z^2 + 340151011200 E^(4 Sqrt[z]) z^2 + 143636613120 z^(5/2) + 143636613120 E^(4 Sqrt[z]) z^(5/2) - 61599605760 z^3 + 61599605760 E^(4 Sqrt[z]) z^3 + 28740096000 z^(7/2) + 28740096000 E^(4 Sqrt[z]) z^(7/2) - 15441592320 z^4 + 15441592320 E^(4 Sqrt[z]) z^4 + 10186260480 z^(9/2) + 10186260480 E^(4 Sqrt[z]) z^(9/2) - 9057337344 z^5 + 9057337344 E^(4 Sqrt[z]) z^5 + 12988710912 z^(11/2) + 12988710912 E^(4 Sqrt[z]) z^(11/2) - 54232350720 z^6 + 54232350720 E^(4 Sqrt[z]) z^6 - 788004864 z^(13/2) - 788004864 E^(4 Sqrt[z]) z^(13/2) + 3177185280 z^7 - 3177185280 E^(4 Sqrt[z]) z^7 + 8388608 z^(15/2) + 8388608 E^(4 Sqrt[z]) z^(15/2) - 33554432 z^8 + 33554432 E^(4 Sqrt[z]) z^8 - 131072 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(25/4) (418209 - 24288 z + 256 z^2) Erf[Sqrt[2] z^(1/4)] - 131072 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(25/4) (418209 - 24288 z + 256 z^2) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z]))

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]