Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9092)

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=-21/4, b_1`>=-11/2

For fixed z and a₁=-21/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.9092.01

Input Form

HypergeometricPFQ[{-(21/4)}, {11/2, 19/4}, z] == (-4 (2086009760120832000 + 4172019520241664000 Sqrt[z] - 403901639132662125 z + 12176190638083426500 z^(3/2) - 1281124565403883200 z^2 + 10305522935170444800 z^(5/2) - 601747814220134400 z^3 + 7347451639249612800 z^(7/2) + 2518002919950336000 z^4 - 11059312996942479360 z^(9/2) - 378867251413647360 z^5 + 1563731265131642880 z^(11/2) + 17028805684101120 z^6 - 68972743407697920 z^(13/2) - 292483246325760 z^7 + 1175812527095808 z^(15/2) + 1974611214336 z^8 - 7911329759232 z^(17/2) - 4294967296 z^9 + 17179869184 z^(19/2) + E^(4 Sqrt[z]) (-2086009760120832000 + 4172019520241664000 Sqrt[z] + 403901639132662125 z + 12176190638083426500 z^(3/2) + 1281124565403883200 z^2 + 10305522935170444800 z^(5/2) + 601747814220134400 z^3 + 7347451639249612800 z^(7/2) - 2518002919950336000 z^4 - 11059312996942479360 z^(9/2) + 378867251413647360 z^5 + 1563731265131642880 z^(11/2) - 17028805684101120 z^6 - 68972743407697920 z^(13/2) + 292483246325760 z^7 + 1175812527095808 z^(15/2) - 1974611214336 z^8 - 7911329759232 z^(17/2) + 4294967296 z^9 + 17179869184 z^(19/2))) - E^(2 Sqrt[z]) Sqrt[2 Pi] z^(3/4) (27820029915006454125 + 52027068931960122000 z + 43243278073317504000 z^2 + 35875904771937484800 z^3 - 45316932343499980800 z^4 + 6304964499965214720 z^5 - 276761130313973760 z^6 + 4709157835898880 z^7 - 31658203938816 z^8 + 68719476736 z^9) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(3/4) (27820029915006454125 + 52027068931960122000 z + 43243278073317504000 z^2 + 35875904771937484800 z^3 - 45316932343499980800 z^4 + 6304964499965214720 z^5 - 276761130313973760 z^6 + 4709157835898880 z^7 - 31658203938816 z^8 + 68719476736 z^9) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z])/ (205859370604387368960 z^(9/2))

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]