Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9096)

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/07.22.03.9096.01

Input Form

HypergeometricPFQ[{-(21/4)}, {11/2, 23/4}, z] == (-4 z^(1/4) (83144900302042044375 + 1000890698054277712500 Sqrt[z] - 141227808645765114000 z + 1032550110541476072000 z^(3/2) - 94653866027710080000 z^2 + 565174474036204032000 z^(5/2) - 33132989912795136000 z^3 + 304655805964571443200 z^(7/2) + 82065229514647142400 z^4 - 355247336841294643200 z^(9/2) - 10158216822757785600 z^5 + 41745875756226969600 z^(11/2) + 389982079879741440 z^6 - 1577134350422507520 z^(13/2) - 5853723670609920 z^7 + 23519520085770240 z^(15/2) + 35111357644800 z^8 - 140651589009408 z^(17/2) - 68719476736 z^9 + 274877906944 z^(19/2) + E^(4 Sqrt[z]) (-83144900302042044375 + 1000890698054277712500 Sqrt[z] + 141227808645765114000 z + 1032550110541476072000 z^(3/2) + 94653866027710080000 z^2 + 565174474036204032000 z^(5/2) + 33132989912795136000 z^3 + 304655805964571443200 z^(7/2) - 82065229514647142400 z^4 - 355247336841294643200 z^(9/2) + 10158216822757785600 z^5 + 41745875756226969600 z^(11/2) - 389982079879741440 z^6 - 1577134350422507520 z^(13/2) + 5853723670609920 z^7 + 23519520085770240 z^(15/2) - 35111357644800 z^8 - 140651589009408 z^(17/2) + 68719476736 z^9 + 274877906944 z^(19/2))) - E^(2 Sqrt[z]) Sqrt[2 Pi] (1251901346175290435625 + 4451204786401032660000 z + 4162165514556809760000 z^2 + 2306308163910266880000 z^3 + 1435036190877499392000 z^4 - 1450141834991999385600 z^5 + 168132386665739059200 z^6 - 6325968692890828800 z^7 + 94183156717977600 z^8 - 562812514467840 z^9 + 1099511627776 z^10) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] (1251901346175290435625 + 4451204786401032660000 z + 4162165514556809760000 z^2 + 2306308163910266880000 z^3 + 1435036190877499392000 z^4 - 1450141834991999385600 z^5 + 168132386665739059200 z^6 - 6325968692890828800 z^7 + 94183156717977600 z^8 - 562812514467840 z^9 + 1099511627776 z^10) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z])/(6934210378253048217600 z^(19/4))

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]