Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9574)

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=-19/4, b_1`>=-11/2

For fixed z and a₁=-19/4, b_1`=7/2

http://functions.wolfram.com/07.22.03.9574.01

Input Form

HypergeometricPFQ[{-(19/4)}, {7/2, 21/4}, z] == (4 z^(1/4) (17494279042865625 + 23325705390487500 Sqrt[z] - 45933696768960000 z + 153572427430329600 z^(3/2) - 65428463376460800 z^2 + 210518409662668800 z^(5/2) - 82398544994304000 z^3 + 427903364741529600 z^(7/2) + 43379764606402560 z^4 - 184647079420231680 z^(9/2) - 4091884465029120 z^5 + 16724981396275200 z^(11/2) + 123565202472960 z^6 - 498197952724992 z^(13/2) - 1327144894464 z^7 + 5321464479744 z^(15/2) + 4294967296 z^8 - 17179869184 z^(17/2) + E^(4 Sqrt[z]) (17494279042865625 - 23325705390487500 Sqrt[z] - 45933696768960000 z - 153572427430329600 z^(3/2) - 65428463376460800 z^2 - 210518409662668800 z^(5/2) - 82398544994304000 z^3 - 427903364741529600 z^(7/2) + 43379764606402560 z^4 + 184647079420231680 z^(9/2) - 4091884465029120 z^5 - 16724981396275200 z^(11/2) + 123565202472960 z^6 + 498197952724992 z^(13/2) - 1327144894464 z^7 - 5321464479744 z^(15/2) + 4294967296 z^8 + 17179869184 z^(17/2))) - E^(2 Sqrt[z]) Sqrt[2 Pi] (17494279042865625 - 64594261081350000 z - 459336967689600000 z^2 - 685943205083136000 z^3 - 1829181880221696000 z^4 + 750433591885824000 z^5 - 67265756135424000 z^6 + 1996757139456000 z^7 - 21298742820864 z^8 + 68719476736 z^9) Erf[Sqrt[2] z^(1/4)] - E^(2 Sqrt[z]) Sqrt[2 Pi] (17494279042865625 - 64594261081350000 z - 459336967689600000 z^2 - 685943205083136000 z^3 - 1829181880221696000 z^4 + 750433591885824000 z^5 - 67265756135424000 z^6 + 1996757139456000 z^7 - 21298742820864 z^8 + 68719476736 z^9) Erfi[Sqrt[2] z^(1/4)])/ E^(2 Sqrt[z])/(6327744393432268800 z^(17/4))

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]