Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9586)

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=-19/4, b_1`>=-11/2

For fixed z and a₁=-19/4, b_1`=9/2

http://functions.wolfram.com/07.22.03.9586.01

Input Form

HypergeometricPFQ[{-(19/4)}, {9/2, -(15/4)}, z] == (149523752503125 - 149523752503125 E^(4 Sqrt[z]) + 299047505006250 Sqrt[z] + 299047505006250 E^(4 Sqrt[z]) Sqrt[z] + 230988417660000 z - 230988417660000 E^(4 Sqrt[z]) z + 63246828645000 z^(3/2) + 63246828645000 E^(4 Sqrt[z]) z^(3/2) - 10119492583200 z^2 + 10119492583200 E^(4 Sqrt[z]) z^2 + 1759911753600 z^(5/2) + 1759911753600 E^(4 Sqrt[z]) z^(5/2) - 335221286400 z^3 + 335221286400 E^(4 Sqrt[z]) z^3 + 70572902400 z^(7/2) + 70572902400 E^(4 Sqrt[z]) z^(7/2) - 16605388800 z^4 + 16605388800 E^(4 Sqrt[z]) z^4 + 4428103680 z^(9/2) + 4428103680 E^(4 Sqrt[z]) z^(9/2) - 1362493440 z^5 + 1362493440 E^(4 Sqrt[z]) z^5 + 495452160 z^(11/2) + 495452160 E^(4 Sqrt[z]) z^(11/2) - 220200960 z^6 + 220200960 E^(4 Sqrt[z]) z^6 + 125829120 z^(13/2) + 125829120 E^(4 Sqrt[z]) z^(13/2) - 100663296 z^7 + 100663296 E^(4 Sqrt[z]) z^7 + 134217728 z^(15/2) + 134217728 E^(4 Sqrt[z]) z^(15/2) - 536870912 z^8 + 536870912 E^(4 Sqrt[z]) z^8 - 536870912 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(33/4) Erf[Sqrt[2] z^(1/4)] - 536870912 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(33/4) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z])/(42211417248000 z^(7/2))

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]