Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8892)

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`=3/2

http://functions.wolfram.com/07.22.03.8892.01

Input Form

HypergeometricPFQ[{-(21/4)}, {3/2, 11/4}, z] == (-4 z^(1/4) (948702429675 + 1264936572900 Sqrt[z] + 20779168606560 z - 126806237873280 z^(3/2) - 23581062731520 z^2 + 104988649651200 z^(5/2) + 4172507136000 z^3 - 17289666035712 z^(7/2) - 211446595584 z^4 + 856201887744 z^(9/2) + 3529506816 z^5 - 14168358912 z^(11/2) - 16777216 z^6 + 67108864 z^(13/2) + E^(4 Sqrt[z]) (-948702429675 + 1264936572900 Sqrt[z] - 20779168606560 z - 126806237873280 z^(3/2) + 23581062731520 z^2 + 104988649651200 z^(5/2) - 4172507136000 z^3 - 17289666035712 z^(7/2) + 211446595584 z^4 + 856201887744 z^(9/2) - 3529506816 z^5 - 14168358912 z^(11/2) + 16777216 z^6 + 67108864 z^(13/2))) - E^(2 Sqrt[z]) Sqrt[2 Pi] (-948702429675 + 35418224041200 z - 566691584659200 z^2 + 431765016883200 z^3 - 69780204748800 z^4 + 3435333156864 z^5 - 56723767296 z^6 + 268435456 z^7) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] (-948702429675 + 35418224041200 z - 566691584659200 z^2 + 431765016883200 z^3 - 69780204748800 z^4 + 3435333156864 z^5 - 56723767296 z^6 + 268435456 z^7) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z])/(1524248661196800 z^(7/4))

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]