Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a98a)

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

For fixed z and a₁=-11/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.a98a.01

Input Form

HypergeometricPFQ[{-(11/4)}, {11/2, 9/4}, z] == (1/(787537920 z^(9/2))) ((4 (-6548850 - 13097700 Sqrt[z] - 7068600 z + 3326400 z^(3/2) + 1663200 z^2 - 5765760 z^(5/2) + 19514880 z^3 - 10114335 z^(7/2) + 52746540 z^4 + 5068080 z^(9/2) - 21198528 z^5 - 322816 z^(11/2) + 1303552 z^6 + 4096 z^(13/2) - 16384 z^7 + E^(4 Sqrt[z]) (6548850 - 13097700 Sqrt[z] + 7068600 z + 3326400 z^(3/2) - 1663200 z^2 - 5765760 z^(5/2) - 19514880 z^3 - 10114335 z^(7/2) - 52746540 z^4 + 5068080 z^(9/2) + 21198528 z^5 - 322816 z^(11/2) - 1303552 z^6 + 4096 z^(13/2) + 16384 z^7)) + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(13/4) (59788575 + 225086400 z - 85747200 z^2 + 5226496 z^3 - 65536 z^4) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(13/4) (59788575 + 225086400 z - 85747200 z^2 + 5226496 z^3 - 65536 z^4) Erfi[Sqrt[2] z^(1/4)])/ E^(2 Sqrt[z]))

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]