Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8434)

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`=9/2

http://functions.wolfram.com/07.22.03.8434.01

Input Form

HypergeometricPFQ[{-(23/4)}, {9/2, -(15/4)}, z] == (3439046307571875 - 3439046307571875 E^(4 Sqrt[z]) + 6878092615143750 Sqrt[z] + 6878092615143750 E^(4 Sqrt[z]) Sqrt[z] + 5122993120245000 z - 5122993120245000 E^(4 Sqrt[z]) z + 1075196086965000 z^(3/2) + 1075196086965000 E^(4 Sqrt[z]) z^(3/2) - 445257673660800 z^2 + 445257673660800 E^(4 Sqrt[z]) z^2 + 121433910998400 z^(5/2) + 121433910998400 E^(4 Sqrt[z]) z^(5/2) - 30840358348800 z^3 + 30840358348800 E^(4 Sqrt[z]) z^3 + 7974737971200 z^(7/2) + 7974737971200 E^(4 Sqrt[z]) z^(7/2) - 2191911321600 z^4 + 2191911321600 E^(4 Sqrt[z]) z^4 + 659787448320 z^(9/2) + 659787448320 E^(4 Sqrt[z]) z^(9/2) - 223448924160 z^5 + 223448924160 E^(4 Sqrt[z]) z^5 + 87695032320 z^(11/2) + 87695032320 E^(4 Sqrt[z]) z^(11/2) - 41397780480 z^6 + 41397780480 E^(4 Sqrt[z]) z^6 + 24788336640 z^(13/2) + 24788336640 E^(4 Sqrt[z]) z^(13/2) - 20535312384 z^7 + 20535312384 E^(4 Sqrt[z]) z^7 + 28051505152 z^(15/2) + 28051505152 E^(4 Sqrt[z]) z^(15/2) - 113816633344 z^8 + 113816633344 E^(4 Sqrt[z]) z^8 - 536870912 z^(17/2) - 536870912 E^(4 Sqrt[z]) z^(17/2) + 2147483648 z^9 - 2147483648 E^(4 Sqrt[z]) z^9 + 134217728 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(33/4) (-851 + 16 z) Erf[Sqrt[2] z^(1/4)] + 134217728 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(33/4) (-851 + 16 z) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z])/(1561822438176000 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]