Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8482)

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/07.22.03.8482.01

Input Form

HypergeometricPFQ[{-(23/4)}, {11/2, -(15/4)}, z] == (-794419697049103125 + 794419697049103125 E^(4 Sqrt[z]) - 1588839394098206250 Sqrt[z] - 1588839394098206250 E^(4 Sqrt[z]) Sqrt[z] - 1306837596877312500 z + 1306837596877312500 E^(4 Sqrt[z]) z - 495222668290350000 z^(3/2) - 495222668290350000 E^(4 Sqrt[z]) z^(3/2) - 37568616215130000 z^2 + 37568616215130000 E^(4 Sqrt[z]) z^2 + 20238985166400000 z^(5/2) + 20238985166400000 E^(4 Sqrt[z]) z^(5/2) - 5424048024595200 z^3 + 5424048024595200 E^(4 Sqrt[z]) z^3 + 1295295050649600 z^(7/2) + 1295295050649600 E^(4 Sqrt[z]) z^(7/2) - 308403583488000 z^4 + 308403583488000 E^(4 Sqrt[z]) z^4 + 76783317811200 z^(9/2) + 76783317811200 E^(4 Sqrt[z]) z^(9/2) - 20590682112000 z^5 + 20590682112000 E^(4 Sqrt[z]) z^5 + 6093070663680 z^(11/2) + 6093070663680 E^(4 Sqrt[z]) z^(11/2) - 2038290186240 z^6 + 2038290186240 E^(4 Sqrt[z]) z^6 + 792723456000 z^(13/2) + 792723456000 E^(4 Sqrt[z]) z^(13/2) - 371699220480 z^7 + 371699220480 E^(4 Sqrt[z]) z^7 + 221459251200 z^(15/2) + 221459251200 E^(4 Sqrt[z]) z^(15/2) - 182804545536 z^8 + 182804545536 E^(4 Sqrt[z]) z^8 + 249108103168 z^(17/2) + 249108103168 E^(4 Sqrt[z]) z^(17/2) - 1009317314560 z^9 + 1009317314560 E^(4 Sqrt[z]) z^9 - 4294967296 z^(19/2) - 4294967296 E^(4 Sqrt[z]) z^(19/2) + 17179869184 z^10 - 17179869184 E^(4 Sqrt[z]) z^10 + 1073741824 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(37/4) (-943 + 16 z) Erf[Sqrt[2] z^(1/4)] + 1073741824 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(37/4) (-943 + 16 z) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z])/ (28459875540096000 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]