Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8374)

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`=5/2

http://functions.wolfram.com/07.22.03.8374.01

Input Form

HypergeometricPFQ[{-(23/4)}, {5/2, 21/4}, z] == (-4 z^(1/4) (2816578925901365625 + 3755438567868487500 Sqrt[z] - 1947875828608710000 z - 4886196993798120000 z^(3/2) + 8686572433418880000 z^2 - 36214854569574912000 z^(5/2) + 23357359856388096000 z^3 - 141840993980089958400 z^(7/2) - 24824371943050444800 z^4 + 109401846586815283200 z^(9/2) + 3934369777818009600 z^5 - 16293372946808832000 z^(11/2) - 197439246292746240 z^6 + 800870712339333120 z^(13/2) + 3800514554757120 z^7 - 15287098571489280 z^(15/2) - 28583007354880 z^8 + 114538187849728 z^(17/2) + 68719476736 z^9 - 274877906944 z^(19/2) + E^(4 Sqrt[z]) (2816578925901365625 - 3755438567868487500 Sqrt[z] - 1947875828608710000 z + 4886196993798120000 z^(3/2) + 8686572433418880000 z^2 + 36214854569574912000 z^(5/2) + 23357359856388096000 z^3 + 141840993980089958400 z^(7/2) - 24824371943050444800 z^4 - 109401846586815283200 z^(9/2) + 3934369777818009600 z^5 + 16293372946808832000 z^(11/2) - 197439246292746240 z^6 - 800870712339333120 z^(13/2) + 3800514554757120 z^7 + 15287098571489280 z^(15/2) - 28583007354880 z^8 - 114538187849728 z^(17/2) + 68719476736 z^9 + 274877906944 z^(19/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] (2816578925901365625 - 4952226682903500000 z + 13205937821076000000 z^2 + 112690669406515200000 z^3 + 631067748676485120000 z^4 - 448759287947722752000 z^5 + 65752276622376960000 z^6 - 3214778994524160000 z^7 + 61233885609984000 z^8 - 458358909829120 z^9 + 1099511627776 z^10) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] (2816578925901365625 - 4952226682903500000 z + 13205937821076000000 z^2 + 112690669406515200000 z^3 + 631067748676485120000 z^4 - 448759287947722752000 z^5 + 65752276622376960000 z^6 - 3214778994524160000 z^7 + 61233885609984000 z^8 - 458358909829120 z^9 + 1099511627776 z^10) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z])/ (2531097757372907520000 z^(17/4))

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]