Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8218)

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`=-1/2

http://functions.wolfram.com/07.22.03.8218.01

Input Form

HypergeometricPFQ[{-(23/4)}, {-(1/2), 9/4}, z] == (4 z^(1/4) (316234143225 + 421645524300 Sqrt[z] + 533326641120 z + 3957936877440 z^(3/2) + 5077559934720 z^2 - 24489469025280 z^(5/2) - 1754545766400 z^3 + 7381302706176 z^(7/2) + 130286026752 z^4 - 529533763584 z^(9/2) - 2854223872 z^5 + 11467227136 z^(11/2) + 16777216 z^6 - 67108864 z^(13/2) + E^(4 Sqrt[z]) (316234143225 - 421645524300 Sqrt[z] + 533326641120 z - 3957936877440 z^(3/2) + 5077559934720 z^2 + 24489469025280 z^(5/2) - 1754545766400 z^3 - 7381302706176 z^(7/2) + 130286026752 z^4 + 529533763584 z^(9/2) - 2854223872 z^5 - 11467227136 z^(11/2) + 16777216 z^6 + 67108864 z^(13/2))) - E^(2 Sqrt[z]) Sqrt[2 Pi] (316234143225 - 5059746291600 z - 26985313555200 z^2 + 102801194496000 z^3 - 29905802035200 z^4 + 2126634811392 z^5 - 45919240192 z^6 + 268435456 z^7) Erf[Sqrt[2] z^(1/4)] - E^(2 Sqrt[z]) Sqrt[2 Pi] (316234143225 - 5059746291600 z - 26985313555200 z^2 + 102801194496000 z^3 - 29905802035200 z^4 + 2126634811392 z^5 - 45919240192 z^6 + 268435456 z^7) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z])/(42046052106240 z^(5/4))

Standard Form

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MathML Form

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Rule 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]