Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8478)

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/07.22.03.8478.01

Input Form

HypergeometricPFQ[{-(23/4)}, {11/2, -(19/4)}, z] == (-29393528790816815625 + 29393528790816815625 E^(4 Sqrt[z]) - 58787057581633631250 Sqrt[z] - 58787057581633631250 E^(4 Sqrt[z]) Sqrt[z] - 49480998273344137500 z + 49480998273344137500 E^(4 Sqrt[z]) z - 20579253104510100000 z^(3/2) - 20579253104510100000 E^(4 Sqrt[z]) z^(3/2) - 3070380543400170000 z^2 + 3070380543400170000 E^(4 Sqrt[z]) z^2 + 396178134632280000 z^(5/2) + 396178134632280000 E^(4 Sqrt[z]) z^(5/2) - 54645259949280000 z^3 + 54645259949280000 E^(4 Sqrt[z]) z^3 + 8095594066560000 z^(7/2) + 8095594066560000 E^(4 Sqrt[z]) z^(7/2) - 1295295050649600 z^4 + 1295295050649600 E^(4 Sqrt[z]) z^4 + 225268704460800 z^(9/2) + 225268704460800 E^(4 Sqrt[z]) z^(9/2) - 42908324659200 z^5 + 42908324659200 E^(4 Sqrt[z]) z^5 + 9033331507200 z^(11/2) + 9033331507200 E^(4 Sqrt[z]) z^(11/2) - 2125489766400 z^6 + 2125489766400 E^(4 Sqrt[z]) z^6 + 566797271040 z^(13/2) + 566797271040 E^(4 Sqrt[z]) z^(13/2) - 174399160320 z^7 + 174399160320 E^(4 Sqrt[z]) z^7 + 63417876480 z^(15/2) + 63417876480 E^(4 Sqrt[z]) z^(15/2) - 28185722880 z^8 + 28185722880 E^(4 Sqrt[z]) z^8 + 16106127360 z^(17/2) + 16106127360 E^(4 Sqrt[z]) z^(17/2) - 12884901888 z^9 + 12884901888 E^(4 Sqrt[z]) z^9 + 17179869184 z^(19/2) + 17179869184 E^(4 Sqrt[z]) z^(19/2) - 68719476736 z^10 + 68719476736 E^(4 Sqrt[z]) z^10 - 68719476736 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(41/4) Erf[Sqrt[2] z^(1/4)] - 68719476736 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(41/4) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z])/ (540737635261824000 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]