Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8278)

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`=1/2

http://functions.wolfram.com/07.22.03.8278.01

Input Form

HypergeometricPFQ[{-(23/4)}, {1/2, 21/4}, z] == (-4 z^(1/4) (641014514170655625 + 854686018894207500 Sqrt[z] + 157788188103546000 z - 310567227378408000 z^(3/2) - 4857356439936000 z^2 + 252582534876672000 z^(5/2) - 181341307090944000 z^3 - 435219137018265600 z^(7/2) - 1293055297693286400 z^4 + 6549860771758080000 z^(9/2) + 612080201288908800 z^5 - 2609718666618470400 z^(11/2) - 59554649698467840 z^6 + 243608272722984960 z^(13/2) + 1865331140198400 z^7 - 7522656693780480 z^(15/2) - 20680267530240 z^8 + 82927228551168 z^(17/2) + 68719476736 z^9 - 274877906944 z^(19/2) + E^(4 Sqrt[z]) (641014514170655625 - 854686018894207500 Sqrt[z] + 157788188103546000 z + 310567227378408000 z^(3/2) - 4857356439936000 z^2 - 252582534876672000 z^(5/2) - 181341307090944000 z^3 + 435219137018265600 z^(7/2) - 1293055297693286400 z^4 - 6549860771758080000 z^(9/2) + 612080201288908800 z^5 + 2609718666618470400 z^(11/2) - 59554649698467840 z^6 - 243608272722984960 z^(13/2) + 1865331140198400 z^7 + 7522656693780480 z^(15/2) - 20680267530240 z^8 - 82927228551168 z^(17/2) + 68719476736 z^9 + 274877906944 z^(19/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] (641014514170655625 - 525960627011820000 z + 382516819644960000 z^2 - 466306218233856000 z^3 + 4352191370182656000 z^4 - 27854024769168998400 z^5 + 10611057054921523200 z^6 - 979953321089433600 z^7 + 30152409879674880 z^8 - 331915072634880 z^9 + 1099511627776 z^10) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] (641014514170655625 - 525960627011820000 z + 382516819644960000 z^2 - 466306218233856000 z^3 + 4352191370182656000 z^4 - 27854024769168998400 z^5 + 10611057054921523200 z^6 - 979953321089433600 z^7 + 30152409879674880 z^8 - 331915072634880 z^9 + 1099511627776 z^10) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z])/ (41894031846172262400 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]