Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8422)

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`=7/2

http://functions.wolfram.com/07.22.03.8422.01

Input Form

HypergeometricPFQ[{-(23/4)}, {7/2, 21/4}, z] == (-4 z^(1/4) (-13278157793535009375 - 17704210391380012500 Sqrt[z] + 40311125198834490000 z - 146172830229701352000 z^(3/2) + 68880758739762816000 z^2 - 229891791459230208000 z^(5/2) + 99164021251147776000 z^3 - 535512089542297190400 z^(7/2) - 64733755380940800000 z^4 + 279277159653428428800 z^(9/2) + 7698903485644800000 z^5 - 31680355831382016000 z^(11/2) - 311119232567869440 z^6 + 1259212828846325760 z^(13/2) + 5021487857664000 z^7 - 20182845892853760 z^(15/2) - 32534377267200 z^8 + 130343667499008 z^(17/2) + 68719476736 z^9 - 274877906944 z^(19/2) + E^(4 Sqrt[z]) (-13278157793535009375 + 17704210391380012500 Sqrt[z] + 40311125198834490000 z + 146172830229701352000 z^(3/2) + 68880758739762816000 z^2 + 229891791459230208000 z^(5/2) + 99164021251147776000 z^3 + 535512089542297190400 z^(7/2) - 64733755380940800000 z^4 - 279277159653428428800 z^(9/2) + 7698903485644800000 z^5 + 31680355831382016000 z^(11/2) - 311119232567869440 z^6 - 1259212828846325760 z^(13/2) + 5021487857664000 z^7 + 20182845892853760 z^(15/2) - 32534377267200 z^8 - 130343667499008 z^(17/2) + 68719476736 z^9 + 274877906944 z^(19/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] (-13278157793535009375 + 54474493511938500000 z + 435795948095508000000 z^2 + 743758418083000320000 z^3 + 2313915078480445440000 z^4 - 1139158192482680832000 z^5 + 127636772266967040000 z^6 - 5051795562823680000 z^7 + 80828729005178880 z^8 - 521580828426240 z^9 + 1099511627776 z^10) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] (-13278157793535009375 + 54474493511938500000 z + 435795948095508000000 z^2 + 743758418083000320000 z^3 + 2313915078480445440000 z^4 - 1139158192482680832000 z^5 + 127636772266967040000 z^6 - 5051795562823680000 z^7 + 80828729005178880 z^8 - 521580828426240 z^9 + 1099511627776 z^10) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z])/(8352622599330594816000 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]