Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8034)

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/07.22.03.8034.01

Input Form

HypergeometricPFQ[{-(23/4)}, {-(9/2), 17/4}, z] == -((13 (-4 z^(1/4) (86358944094971625 + 115145258793295500 Sqrt[z] + 47543848792070400 z - 6791978398867200 z^(3/2) - 3018657066163200 z^2 + 9513343481241600 z^(5/2) - 1075328005570560 z^3 + 3737647557181440 z^(7/2) - 151404358533120 z^4 + 560583805501440 z^(9/2) - 12930452029440 z^5 + 49140247560192 z^(11/2) - 828056272896 z^6 + 3201898119168 z^(13/2) - 51539607552 z^7 + 219043332096 z^(15/2) + 4294967296 z^8 - 17179869184 z^(17/2) + E^(4 Sqrt[z]) (86358944094971625 - 115145258793295500 Sqrt[z] + 47543848792070400 z + 6791978398867200 z^(3/2) - 3018657066163200 z^2 - 9513343481241600 z^(5/2) - 1075328005570560 z^3 - 3737647557181440 z^(7/2) - 151404358533120 z^4 - 560583805501440 z^(9/2) - 12930452029440 z^5 - 49140247560192 z^(11/2) - 828056272896 z^6 - 3201898119168 z^(13/2) - 51539607552 z^7 - 219043332096 z^(15/2) + 4294967296 z^8 + 17179869184 z^(17/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] (86358944094971625 - 44572358242566000 z + 21130599463142400 z^2 - 34298944056115200 z^3 - 14441660655206400 z^4 - 2200634004602880 z^5 - 193995284152320 z^6 - 12669079781376 z^7 - 889058230272 z^8 + 68719476736 z^9) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] (86358944094971625 - 44572358242566000 z + 21130599463142400 z^2 - 34298944056115200 z^3 - 14441660655206400 z^4 - 2200634004602880 z^5 - 193995284152320 z^6 - 12669079781376 z^7 - 889058230272 z^8 + 68719476736 z^9) Erfi[Sqrt[2] z^(1/4)]))/E^(2 Sqrt[z])/(2094701592308613120 z^(13/4)))

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]