Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8326)

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`=3/2

http://functions.wolfram.com/07.22.03.8326.01

Input Form

HypergeometricPFQ[{-(23/4)}, {3/2, 21/4}, z] == (-4 z^(1/4) (-1068357523617759375 - 1424476698157012500 Sqrt[z] + 55783702864890000 z + 942630734125080000 z^(3/2) - 380492921128320000 z^2 - 1198147921850880000 z^(5/2) + 2720119606364160000 z^3 - 22785979839514214400 z^(7/2) - 7332758772911308800 z^4 + 33603871050576691200 z^(9/2) + 1741227564780748800 z^5 - 7284757050792345600 z^(11/2) - 115273595973795840 z^6 + 469092702848286720 z^(13/2) + 2748462315601920 z^7 - 11067035505131520 z^(15/2) - 24631637442560 z^8 + 98732708200448 z^(17/2) + 68719476736 z^9 - 274877906944 z^(19/2) + E^(4 Sqrt[z]) (-1068357523617759375 + 1424476698157012500 Sqrt[z] + 55783702864890000 z - 942630734125080000 z^(3/2) - 380492921128320000 z^2 + 1198147921850880000 z^(5/2) + 2720119606364160000 z^3 + 22785979839514214400 z^(7/2) - 7332758772911308800 z^4 - 33603871050576691200 z^(9/2) + 1741227564780748800 z^5 + 7284757050792345600 z^(11/2) - 115273595973795840 z^6 - 469092702848286720 z^(13/2) + 2748462315601920 z^7 + 11067035505131520 z^(15/2) - 24631637442560 z^8 - 98732708200448 z^(17/2) + 68719476736 z^9 + 274877906944 z^(19/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] (-1068357523617759375 + 1195365061390500000 z - 1366131498732000000 z^2 + 3885885151948800000 z^3 + 108804784254566400000 z^4 - 139270123845844992000 z^5 + 29475158485893120000 z^6 - 1884525617479680000 z^7 + 44341779234816000 z^8 - 395136991232000 z^9 + 1099511627776 z^10) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] (-1068357523617759375 + 1195365061390500000 z - 1366131498732000000 z^2 + 3885885151948800000 z^3 + 108804784254566400000 z^4 - 139270123845844992000 z^5 + 29475158485893120000 z^6 - 1884525617479680000 z^7 + 44341779234816000 z^8 - 395136991232000 z^9 + 1099511627776 z^10) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z])/(523675398077153280000 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]