Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8984)

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`=7/2

http://functions.wolfram.com/07.22.03.8984.01

Input Form

HypergeometricPFQ[{-(21/4)}, {7/2, 7/4}, z] == (-4 (-86612198400 - 173224396800 Sqrt[z] + 423437414400 z + 1077840691200 z^(3/2) + 4641261636375 z^2 - 25343217518220 z^(5/2) - 3297698444880 z^3 + 14351263698240 z^(7/2) + 441139668480 z^4 - 1816403097600 z^(9/2) - 18122711040 z^5 + 73245032448 z^(11/2) + 255000576 z^6 - 1023148032 z^(13/2) - 1048576 z^7 + 4194304 z^(15/2) + E^(4 Sqrt[z]) (86612198400 - 173224396800 Sqrt[z] - 423437414400 z + 1077840691200 z^(3/2) - 4641261636375 z^2 - 25343217518220 z^(5/2) + 3297698444880 z^3 + 14351263698240 z^(7/2) - 441139668480 z^4 - 1816403097600 z^(9/2) + 18122711040 z^5 + 73245032448 z^(11/2) - 255000576 z^6 - 1023148032 z^(13/2) + 1048576 z^7 + 4194304 z^(15/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(7/4) (-12604189422825 + 110000198599200 z - 58666772586240 z^2 + 7319051550720 z^3 - 293741199360 z^4 + 4095737856 z^5 - 16777216 z^6) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(7/4) (12604189422825 - 110000198599200 z + 58666772586240 z^2 - 7319051550720 z^3 + 293741199360 z^4 - 4095737856 z^5 + 16777216 z^6) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z])/(332238575370240 z^(5/2))

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]