Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9032)

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/07.22.03.9032.01

Input Form

HypergeometricPFQ[{-(21/4)}, {9/2, 7/4}, z] == (-4 (378928368000 + 757856736000 Sqrt[z] - 1010475648000 z^(3/2) + 1347300864000 z^2 + 4311362764800 z^(5/2) + 11632114104975 z^3 - 60034582622700 z^(7/2) - 6180665374800 z^4 + 26531753774400 z^(9/2) + 674826647040 z^5 - 2767036446720 z^(11/2) - 23531397120 z^6 + 94978867200 z^(13/2) + 288030720 z^7 - 1155268608 z^(15/2) - 1048576 z^8 + 4194304 z^(17/2) + E^(4 Sqrt[z]) (-378928368000 + 757856736000 Sqrt[z] - 1010475648000 z^(3/2) - 1347300864000 z^2 + 4311362764800 z^(5/2) - 11632114104975 z^3 - 60034582622700 z^(7/2) + 6180665374800 z^4 + 26531753774400 z^(9/2) - 674826647040 z^5 - 2767036446720 z^(11/2) + 23531397120 z^6 + 94978867200 z^(13/2) - 288030720 z^7 - 1155268608 z^(15/2) + 1048576 z^8 + 4194304 z^(17/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(11/4) (-40104239072625 + 256667130064800 z - 108070370553600 z^2 + 11137687142400 z^3 - 380775628800 z^4 + 4624220160 z^5 - 16777216 z^6) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(11/4) (40104239072625 - 256667130064800 z + 108070370553600 z^2 - 11137687142400 z^3 + 380775628800 z^4 - 4624220160 z^5 + 16777216 z^6) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z])/(830596438425600 z^(7/2))

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]