Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9614)

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=-19/4, b_1`>=-11/2

For fixed z and a₁=-19/4, b_1`=9/2

http://functions.wolfram.com/07.22.03.9614.01

Input Form

HypergeometricPFQ[{-(19/4)}, {9/2, 13/4}, z] == (4 (-10193154048000 - 20386308096000 Sqrt[z] + 114163325337600 z - 73443860703675 z^(3/2) + 257249642334300 z^2 - 125829045064800 z^(5/2) + 696012044112000 z^3 + 89952383727360 z^(7/2) - 387668353121280 z^4 - 10417227448320 z^(9/2) + 42736650485760 z^5 + 371114311680 z^(11/2) - 1498043645952 z^6 - 4586471424 z^(13/2) + 18396217344 z^7 + 16777216 z^(15/2) - 67108864 z^8 + E^(4 Sqrt[z]) (10193154048000 - 20386308096000 Sqrt[z] - 114163325337600 z - 73443860703675 z^(3/2) - 257249642334300 z^2 - 125829045064800 z^(5/2) - 696012044112000 z^3 + 89952383727360 z^(7/2) + 387668353121280 z^4 - 10417227448320 z^(9/2) - 42736650485760 z^5 + 371114311680 z^(11/2) + 1498043645952 z^6 - 4586471424 z^(13/2) - 18396217344 z^7 + 16777216 z^(15/2) + 67108864 z^8)) + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(5/4) (328952255506875 + 818725613706000 z + 3022986881376000 z^2 - 1580646735360000 z^3 + 172043182080000 z^4 - 6005871083520 z^5 + 73635201024 z^6 - 268435456 z^7) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(5/4) (328952255506875 + 818725613706000 z + 3022986881376000 z^2 - 1580646735360000 z^3 + 172043182080000 z^4 - 6005871083520 z^5 + 73635201024 z^6 - 268435456 z^7) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z])/(11177242184908800 z^(7/2))

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]