Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a98e)

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=-11/4, b_1`>=-11/2

For fixed z and a₁=-11/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.a98e.01

Input Form

HypergeometricPFQ[{-(11/4)}, {11/2, 13/4}, z] == (1/(84004044800 z^(9/2))) ((3 (4 (232848000 + 465696000 Sqrt[z] + 79833600 z - 461260800 z^(3/2) + 1312819200 z^2 - 480023775 z^(5/2) + 1441555500 z^3 - 450690240 z^(7/2) + 2153733120 z^4 + 137029120 z^(9/2) - 566855680 z^5 - 6471680 z^(11/2) + 26083328 z^6 + 65536 z^(13/2) - 262144 z^7 + E^(4 Sqrt[z]) (-232848000 + 465696000 Sqrt[z] - 79833600 z - 461260800 z^(3/2) - 1312819200 z^2 - 480023775 z^(5/2) - 1441555500 z^3 - 450690240 z^(7/2) - 2153733120 z^4 + 137029120 z^(9/2) + 566855680 z^5 - 6471680 z^(11/2) - 26083328 z^6 + 65536 z^(13/2) + 262144 z^7)) + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(9/4) (3886257375 + 4783086000 z + 9003456000 z^2 - 2286592000 z^3 + 104529920 z^4 - 1048576 z^5) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(9/4) (3886257375 + 4783086000 z + 9003456000 z^2 - 2286592000 z^3 + 104529920 z^4 - 1048576 z^5) Erfi[Sqrt[2] z^(1/4)]))/E^(2 Sqrt[z]))

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]