Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8796)

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`=-1/2

http://functions.wolfram.com/07.22.03.8796.01

Input Form

HypergeometricPFQ[{-(21/4)}, {-(1/2), 11/4}, z] == (4 z^(1/4) (97692469875 + 130256626500 Sqrt[z] - 301037536800 z + 1263213705600 z^(3/2) - 808142227200 z^2 + 4722370329600 z^(5/2) + 700440330240 z^3 - 3016663695360 z^(7/2) - 78962688000 z^4 + 322566881280 z^(9/2) + 2296381440 z^5 - 9235857408 z^(11/2) - 16777216 z^6 + 67108864 z^(13/2) + E^(4 Sqrt[z]) (-97692469875 + 130256626500 Sqrt[z] + 301037536800 z + 1263213705600 z^(3/2) + 808142227200 z^2 + 4722370329600 z^(5/2) - 700440330240 z^3 - 3016663695360 z^(7/2) + 78962688000 z^4 + 322566881280 z^(9/2) - 2296381440 z^5 - 9235857408 z^(11/2) + 16777216 z^6 + 67108864 z^(13/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] (-97692469875 + 405242838000 z + 3890331244800 z^2 + 20748433305600 z^3 - 12295367884800 z^4 + 1297093754880 z^5 - 36993761280 z^6 + 268435456 z^7) Erf[Sqrt[2] z^(1/4)] - E^(2 Sqrt[z]) Sqrt[2 Pi] (-97692469875 + 405242838000 z + 3890331244800 z^2 + 20748433305600 z^3 - 12295367884800 z^4 + 1297093754880 z^5 - 36993761280 z^6 + 268435456 z^7) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z])/(13951932825600 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]