Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a7wg)

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=-17/4, b_1`>=-11/2

For fixed z and a₁=-17/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.a7wg.01

Input Form

HypergeometricPFQ[{-(17/4)}, {11/2, 15/4}, z] == (4 (16167610368000 + 32335220736000 Sqrt[z] - 21556813824000 z - 86227255296000 z^(3/2) + 10010353318875 z^2 - 147610405460700 z^(5/2) + 8515362492000 z^3 - 136935088617600 z^(7/2) - 53290828281600 z^4 + 234390586752000 z^(9/2) + 8059453194240 z^5 - 33172552089600 z^(11/2) - 325973114880 z^6 + 1316774215680 z^(13/2) + 4351590400 z^7 - 17456693248 z^(15/2) - 16777216 z^8 + 67108864 z^(17/2) + E^(4 Sqrt[z]) (-16167610368000 + 32335220736000 Sqrt[z] + 21556813824000 z - 86227255296000 z^(3/2) - 10010353318875 z^2 - 147610405460700 z^(5/2) - 8515362492000 z^3 - 136935088617600 z^(7/2) + 53290828281600 z^4 + 234390586752000 z^(9/2) - 8059453194240 z^5 - 33172552089600 z^(11/2) + 325973114880 z^6 + 1316774215680 z^(13/2) - 4351590400 z^7 - 17456693248 z^(15/2) + 16777216 z^8 + 67108864 z^(17/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(7/4) (-441146629798875 - 641667825162000 z - 684445680172800 z^2 + 960625516032000 z^3 - 133652245708800 z^4 + 5280088719360 z^5 - 69877104640 z^6 + 268435456 z^7) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(7/4) (441146629798875 + 641667825162000 z + 684445680172800 z^2 - 960625516032000 z^3 + 133652245708800 z^4 - 5280088719360 z^5 + 69877104640 z^6 - 268435456 z^7) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z])/(4295609863372800 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]