Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a98i)

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=-11/4, b_1`>=-11/2

For fixed z and a₁=-11/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.a98i.01

Input Form

HypergeometricPFQ[{-(11/4)}, {11/2, 17/4}, z] == (1/(827116748800 z^(9/2))) ((4 (-17882726400 - 35765452800 Sqrt[z] + 112405708800 z - 42288159375 z^(3/2) + 111656645100 z^2 - 22156651440 z^(5/2) + 66418672320 z^3 - 15219832320 z^(7/2) + 69650380800 z^4 + 3316162560 z^(9/2) - 13627195392 z^5 - 124452864 z^(11/2) + 500957184 z^6 + 1048576 z^(13/2) - 4194304 z^7 + E^(4 Sqrt[z]) (17882726400 - 35765452800 Sqrt[z] - 112405708800 z - 42288159375 z^(3/2) - 111656645100 z^2 - 22156651440 z^(5/2) - 66418672320 z^3 - 15219832320 z^(7/2) - 69650380800 z^4 + 3316162560 z^(9/2) + 13627195392 z^5 - 124452864 z^(11/2) - 500957184 z^6 + 1048576 z^(13/2) + 4194304 z^7)) + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(5/4) (314786847375 + 373080708000 z + 229588128000 z^2 + 288110592000 z^3 - 54878208000 z^4 + 2006974464 z^5 - 16777216 z^6) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(5/4) (314786847375 + 373080708000 z + 229588128000 z^2 + 288110592000 z^3 - 54878208000 z^4 + 2006974464 z^5 - 16777216 z^6) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z]))

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]