Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8568)

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`=-11/2

http://functions.wolfram.com/07.22.03.8568.01

Input Form

HypergeometricPFQ[{-(21/4)}, {-(11/2), 23/4}, z] == (19 (4 z^(1/4) (-5485155330348559490625 - 7313540440464745987500 Sqrt[z] - 4423800071305504890000 z - 1440623064695494680000 z^(3/2) - 216205881419848320000 z^2 - 7123752270835200000 z^(5/2) - 2324767640832000000 z^3 + 4537946434904064000 z^(7/2) - 835930126467072000 z^4 + 2961570555533721600 z^(9/2) - 97495502133657600 z^5 + 370351639049011200 z^(11/2) - 5666831188623360 z^6 + 22017587470663680 z^(13/2) - 198540231966720 z^7 + 779729837752320 z^(15/2) - 4574140170240 z^8 + 18090402250752 z^(17/2) - 68719476736 z^9 + 274877906944 z^(19/2) + E^(4 Sqrt[z]) (5485155330348559490625 - 7313540440464745987500 Sqrt[z] + 4423800071305504890000 z - 1440623064695494680000 z^(3/2) + 216205881419848320000 z^2 - 7123752270835200000 z^(5/2) + 2324767640832000000 z^3 + 4537946434904064000 z^(7/2) + 835930126467072000 z^4 + 2961570555533721600 z^(9/2) + 97495502133657600 z^5 + 370351639049011200 z^(11/2) + 5666831188623360 z^6 + 22017587470663680 z^(13/2) + 198540231966720 z^7 + 779729837752320 z^(15/2) + 4574140170240 z^8 + 18090402250752 z^(17/2) + 68719476736 z^9 + 274877906944 z^(19/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] (5485155330348559490625 - 1427032281066291900000 z + 252447971097722400000 z^2 - 46628196681830400000 z^3 + 15006775943577600000 z^4 + 11525203924667596800 z^5 + 1463517958687948800 z^6 + 87455788380979200 z^7 + 3104939232460800 z^8 + 72155450572800 z^9 + 1099511627776 z^10) Erf[Sqrt[2] z^(1/4)] - E^(2 Sqrt[z]) Sqrt[2 Pi] (5485155330348559490625 - 1427032281066291900000 z + 252447971097722400000 z^2 - 46628196681830400000 z^3 + 15006775943577600000 z^4 + 11525203924667596800 z^5 + 1463517958687948800 z^6 + 87455788380979200 z^7 + 3104939232460800 z^8 + 72155450572800 z^9 + 1099511627776 z^10) Erfi[Sqrt[2] z^(1/4)]))/E^(2 Sqrt[z])/(1532124593231442739200 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]