Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9048)

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`=9/2

http://functions.wolfram.com/07.22.03.9048.01

Input Form

HypergeometricPFQ[{-(21/4)}, {9/2, 23/4}, z] == (-4 z^(1/4) (32100034517315139375 + 42800046023086852500 Sqrt[z] - 3006903599977914000 z + 173338766611074792000 z^(3/2) - 18596560405917312000 z^2 + 154624620627509760000 z^(5/2) - 9025272081745920000 z^3 + 112761878029620019200 z^(7/2) + 39216836903937638400 z^4 - 172377255928253644800 z^(9/2) - 5956841643127603200 z^5 + 24590823946872422400 z^(11/2) + 269447527126794240 z^6 - 1091421062320619520 z^(13/2) - 4649629589176320 z^7 + 18692320442449920 z^(15/2) + 31503585116160 z^8 - 126220498894848 z^(17/2) - 68719476736 z^9 + 274877906944 z^(19/2) + E^(4 Sqrt[z]) (-32100034517315139375 + 42800046023086852500 Sqrt[z] + 3006903599977914000 z + 173338766611074792000 z^(3/2) + 18596560405917312000 z^2 + 154624620627509760000 z^(5/2) + 9025272081745920000 z^3 + 112761878029620019200 z^(7/2) - 39216836903937638400 z^4 - 172377255928253644800 z^(9/2) + 5956841643127603200 z^5 + 24590823946872422400 z^(11/2) - 269447527126794240 z^6 - 1091421062320619520 z^(13/2) + 4649629589176320 z^7 + 18692320442449920 z^(15/2) - 31503585116160 z^8 - 126220498894848 z^(17/2) + 68719476736 z^9 + 274877906944 z^(19/2))) - E^(2 Sqrt[z]) Sqrt[2 Pi] (-32100034517315139375 + 342400368184694820000 z + 747055348766606880000 z^2 + 650497174436229120000 z^3 + 551936996491345920000 z^4 - 706479355508922777600 z^5 + 99154997264410214400 z^6 - 4379516787385958400 z^7 + 74863534827110400 z^8 - 505088154009600 z^9 + 1099511627776 z^10) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] (-32100034517315139375 + 342400368184694820000 z + 747055348766606880000 z^2 + 650497174436229120000 z^3 + 551936996491345920000 z^4 - 706479355508922777600 z^5 + 99154997264410214400 z^6 - 4379516787385958400 z^7 + 74863534827110400 z^8 - 505088154009600 z^9 + 1099511627776 z^10) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z])/(3200404789962945331200 z^(19/4))

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]