Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8386)

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/07.22.03.8386.01

Input Form

HypergeometricPFQ[{-(23/4)}, {7/2, -(15/4)}, z] == (-23717560741875 + 23717560741875 E^(4 Sqrt[z]) - 47435121483750 Sqrt[z] - 47435121483750 E^(4 Sqrt[z]) Sqrt[z] - 26563668030900 z + 26563668030900 E^(4 Sqrt[z]) z + 10119492583200 z^(3/2) + 10119492583200 E^(4 Sqrt[z]) z^(3/2) - 2891283595200 z^2 + 2891283595200 E^(4 Sqrt[z]) z^2 + 793945152000 z^(5/2) + 793945152000 E^(4 Sqrt[z]) z^(5/2) - 226248422400 z^3 + 226248422400 E^(4 Sqrt[z]) z^3 + 69742632960 z^(7/2) + 69742632960 E^(4 Sqrt[z]) z^(7/2) - 24013946880 z^4 + 24013946880 E^(4 Sqrt[z]) z^4 + 9537454080 z^(9/2) + 9537454080 E^(4 Sqrt[z]) z^(9/2) - 4541644800 z^5 + 4541644800 E^(4 Sqrt[z]) z^5 + 2736783360 z^(11/2) + 2736783360 E^(4 Sqrt[z]) z^(11/2) - 2277507072 z^6 + 2277507072 E^(4 Sqrt[z]) z^6 + 3120562176 z^(13/2) + 3120562176 E^(4 Sqrt[z]) z^(13/2) - 12683575296 z^7 + 12683575296 E^(4 Sqrt[z]) z^7 - 67108864 z^(15/2) - 67108864 E^(4 Sqrt[z]) z^(15/2) + 268435456 z^8 - 268435456 E^(4 Sqrt[z]) z^8 + 16777216 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(29/4) (-759 + 16 z) Erf[Sqrt[2] z^(1/4)] + 16777216 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(29/4) (-759 + 16 z) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z])/ (73869980184000 z^(5/2))

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]