Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9084)

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`=11/2

http://functions.wolfram.com/07.22.03.9084.01

Input Form

HypergeometricPFQ[{-(21/4)}, {11/2, 11/4}, z] == (-4 (148539920256000 + 297079840512000 Sqrt[z] + 60628538880000 z - 274849376256000 z^(3/2) + 177843714048000 z^2 + 827781650841600 z^(5/2) + 67548520842075 z^3 + 2021555213086500 z^(7/2) + 1527832864303200 z^4 - 7095198966710400 z^(9/2) - 403474928613120 z^5 + 1690257229839360 z^(11/2) + 27546494976000 z^6 - 112121092177920 z^(13/2) - 665082593280 z^7 + 2678144630784 z^(15/2) + 5995757568 z^8 - 24033361920 z^(17/2) - 16777216 z^9 + 67108864 z^(19/2) + E^(4 Sqrt[z]) (-148539920256000 + 297079840512000 Sqrt[z] - 60628538880000 z - 274849376256000 z^(3/2) - 177843714048000 z^2 + 827781650841600 z^(5/2) - 67548520842075 z^3 + 2021555213086500 z^(7/2) - 1527832864303200 z^4 - 7095198966710400 z^(9/2) + 403474928613120 z^5 + 1690257229839360 z^(11/2) - 27546494976000 z^6 - 112121092177920 z^(13/2) + 665082593280 z^7 + 2678144630784 z^(15/2) - 5995757568 z^8 - 24033361920 z^(17/2) + 16777216 z^9 + 67108864 z^(19/2))) - E^(2 Sqrt[z]) Sqrt[2 Pi] z^(11/4) (4692195971497125 + 11678354417948400 z - 29503211161132800 z^2 + 6841324327219200 z^3 - 450457568870400 z^4 + 10730502881280 z^5 - 96183779328 z^6 + 268435456 z^7) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(11/4) (4692195971497125 + 11678354417948400 z - 29503211161132800 z^2 + 6841324327219200 z^3 - 450457568870400 z^4 + 10730502881280 z^5 - 96183779328 z^6 + 268435456 z^7) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z])/ (115176039461683200 z^(9/2))

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]