Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8616)

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/07.22.03.8616.01

Input Form

HypergeometricPFQ[{-(21/4)}, {-(9/2), 23/4}, z] == (209 (4 z^(1/4) (-133784276349964865625 - 178379035133286487500 Sqrt[z] - 104134788077810490000 z - 30120115070125080000 z^(3/2) - 2752358831913600000 z^2 + 129522768560640000 z^(5/2) - 158954555934720000 z^3 + 198990948409344000 z^(7/2) - 42984286765056000 z^4 + 142432168299724800 z^(9/2) - 5920247041228800 z^5 + 21890701511884800 z^(11/2) - 446271596789760 z^6 + 1700190989844480 z^(13/2) - 22661321195520 z^7 + 87037512253440 z^(15/2) - 966367641600 z^8 + 3659312136192 z^(17/2) - 68719476736 z^9 + 274877906944 z^(19/2) + E^(4 Sqrt[z]) (133784276349964865625 - 178379035133286487500 Sqrt[z] + 104134788077810490000 z - 30120115070125080000 z^(3/2) + 2752358831913600000 z^2 + 129522768560640000 z^(5/2) + 158954555934720000 z^3 + 198990948409344000 z^(7/2) + 42984286765056000 z^4 + 142432168299724800 z^(9/2) + 5920247041228800 z^5 + 21890701511884800 z^(11/2) + 446271596789760 z^6 + 1700190989844480 z^(13/2) + 22661321195520 z^7 + 87037512253440 z^(15/2) + 966367641600 z^8 + 3659312136192 z^(17/2) + 68719476736 z^9 + 274877906944 z^(19/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] (133784276349964865625 - 38568440028818700000 z + 7649938518112800000 z^2 - 1607868851097600000 z^3 + 600271037743104000 z^4 + 548819234507980800 z^5 + 86089291687526400 z^6 + 6727368336998400 z^7 + 344993248051200 z^8 + 14431090114560 z^9 + 1099511627776 z^10) Erf[Sqrt[2] z^(1/4)] - E^(2 Sqrt[z]) Sqrt[2 Pi] (133784276349964865625 - 38568440028818700000 z + 7649938518112800000 z^2 - 1607868851097600000 z^3 + 600271037743104000 z^4 + 548819234507980800 z^5 + 86089291687526400 z^6 + 6727368336998400 z^7 + 344993248051200 z^8 + 14431090114560 z^9 + 1099511627776 z^10) Erfi[Sqrt[2] z^(1/4)]))/ E^(2 Sqrt[z])/(766062296615721369600 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]