Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9028)

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/07.22.03.9028.01

Input Form

HypergeometricPFQ[{-(21/4)}, {9/2, 3/4}, z] == (1/(6489034675200 z^(7/2))) ((-4 (-10854718875 - 21709437750 Sqrt[z] - 7894341000 z + 13157235000 z^(3/2) - 25261891200 z^(5/2) + 89820057600 z^3 - 590188032000 z^(7/2) - 123521162625 z^4 + 548033692500 z^(9/2) + 20877071040 z^5 - 86293509120 z^(11/2) - 977733120 z^6 + 3955230720 z^(13/2) + 14991360 z^7 - 60162048 z^(15/2) - 65536 z^8 + 262144 z^(17/2) + E^(4 Sqrt[z]) (10854718875 - 21709437750 Sqrt[z] + 7894341000 z + 13157235000 z^(3/2) - 25261891200 z^(5/2) - 89820057600 z^3 - 590188032000 z^(7/2) + 123521162625 z^4 + 548033692500 z^(9/2) - 20877071040 z^5 - 86293509120 z^(11/2) + 977733120 z^6 + 3955230720 z^(13/2) - 14991360 z^7 - 60162048 z^(15/2) + 65536 z^8 + 262144 z^(17/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(15/4) (2673615938175 - 2251466053200 z + 348052723200 z^2 - 15865651200 z^3 + 240844800 z^4 - 1048576 z^5) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(15/4) (-2673615938175 + 2251466053200 z - 348052723200 z^2 + 15865651200 z^3 - 240844800 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]