Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8458)

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=-23/4, b_1`>=-11/2

For fixed z and a₁=-23/4, b_1`=9/2

http://functions.wolfram.com/07.22.03.8458.01

Input Form

HypergeometricPFQ[{-(23/4)}, {9/2, 9/4}, z] == (-4 (-73263294720000 - 146526589440000 Sqrt[z] + 70332762931200 z + 336034311782400 z^(3/2) - 2000576367820800 z^2 + 1719555826544325 z^(5/2) - 11711293472686500 z^3 - 2718152104963680 z^(7/2) + 12229533043136640 z^4 + 543227609675520 z^(9/2) - 2263824090823680 z^5 - 32608777420800 z^(11/2) + 132558185496576 z^6 + 728544509952 z^(13/2) - 2932696940544 z^7 - 6230638592 z^(15/2) + 24972886016 z^8 + 16777216 z^(17/2) - 67108864 z^9 + E^(4 Sqrt[z]) (73263294720000 - 146526589440000 Sqrt[z] - 70332762931200 z + 336034311782400 z^(3/2) + 2000576367820800 z^2 + 1719555826544325 z^(5/2) + 11711293472686500 z^3 - 2718152104963680 z^(7/2) - 12229533043136640 z^4 + 543227609675520 z^(9/2) + 2263824090823680 z^5 - 32608777420800 z^(11/2) - 132558185496576 z^6 + 728544509952 z^(13/2) + 2932696940544 z^7 - 6230638592 z^(15/2) - 24972886016 z^8 + 16777216 z^(17/2) + 67108864 z^9)) + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(9/4) (6220852654141125 + 53595038251062000 z - 50442388942176000 z^2 + 9150546746880000 z^3 - 532395447091200 z^4 + 11749416763392 z^5 - 99941875712 z^6 + 268435456 z^7) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(9/4) (6220852654141125 + 53595038251062000 z - 50442388942176000 z^2 + 9150546746880000 z^3 - 532395447091200 z^4 + 11749416763392 z^5 - 99941875712 z^6 + 268435456 z^7) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z])/ (232626352973414400 z^(7/2))

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]