Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8134)

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`=-5/2

http://functions.wolfram.com/07.22.03.8134.01

Input Form

HypergeometricPFQ[{-(23/4)}, {-(5/2), 21/4}, z] == -((221 (-4 z^(1/4) (-1629676848243819375 - 2172902464325092500 Sqrt[z] - 995449334083974000 z - 2829990999528000 z^(3/2) + 92528401375872000 z^2 - 52259754742272000 z^(5/2) - 7719858026496000 z^3 + 57244170667622400 z^(7/2) - 8015561913139200 z^4 + 32607889116364800 z^(9/2) - 2080529606246400 z^5 + 8711322992640000 z^(11/2) - 401716008714240 z^6 + 2211182039531520 z^(13/2) + 229463996497920 z^7 - 943625789767680 z^(15/2) - 8826157793280 z^8 + 35510789603328 z^(17/2) + 68719476736 z^9 - 274877906944 z^(19/2) + E^(4 Sqrt[z]) (-1629676848243819375 + 2172902464325092500 Sqrt[z] - 995449334083974000 z + 2829990999528000 z^(3/2) + 92528401375872000 z^2 + 52259754742272000 z^(5/2) - 7719858026496000 z^3 - 57244170667622400 z^(7/2) - 8015561913139200 z^4 - 32607889116364800 z^(9/2) - 2080529606246400 z^5 - 8711322992640000 z^(11/2) - 401716008714240 z^6 - 2211182039531520 z^(13/2) + 229463996497920 z^7 + 943625789767680 z^(15/2) - 8826157793280 z^8 - 35510789603328 z^(17/2) + 68719476736 z^9 + 274877906944 z^(19/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] (-1629676848243819375 + 742872637376100000 z - 258390482565600000 z^2 + 116049058836480000 z^3 - 216624909828096000 z^4 - 126036311172710400 z^5 - 34295594876928000 z^6 - 9501809836032000 z^7 + 3800723934412800 z^8 - 142249316843520 z^9 + 1099511627776 z^10) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] (-1629676848243819375 + 742872637376100000 z - 258390482565600000 z^2 + 116049058836480000 z^3 - 216624909828096000 z^4 - 126036311172710400 z^5 - 34295594876928000 z^6 - 9501809836032000 z^7 + 3800723934412800 z^8 - 142249316843520 z^9 + 1099511627776 z^10) Erfi[Sqrt[2] z^(1/4)]))/E^(2 Sqrt[z])/ (239394467692412928000 z^(17/4)))

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]