Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a9go)

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=-9/4, b_1`>=-11/2

For fixed z and a₁=-9/4, b_1`=-1/2

http://functions.wolfram.com/07.22.03.a9go.01

Input Form

HypergeometricPFQ[{-(9/4)}, {-(1/2), 23/4}, z] == -((209 (4 z^(1/4) (97692469875 + 130256626500 Sqrt[z] + 69470200800 z + 13232419200 z^(3/2) - 1669973760 z^2 + 339655680 z^(5/2) + 449003520 z^3 - 681246720 z^(7/2) + 309657600 z^4 - 864288768 z^(9/2) + 182452224 z^5 - 780140544 z^(11/2) - 16777216 z^6 + 67108864 z^(13/2) + E^(4 Sqrt[z]) (-97692469875 + 130256626500 Sqrt[z] - 69470200800 z + 13232419200 z^(3/2) + 1669973760 z^2 + 339655680 z^(5/2) - 449003520 z^3 - 681246720 z^(7/2) - 309657600 z^4 - 864288768 z^(9/2) - 182452224 z^5 - 780140544 z^(11/2) + 16777216 z^6 + 67108864 z^(13/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] (-97692469875 + 34735100400 z - 8915961600 z^2 + 2612736000 z^3 - 1548288000 z^4 - 2972712960 z^5 - 3170893824 z^6 + 268435456 z^7) Erf[Sqrt[2] z^(1/4)] - E^(2 Sqrt[z]) Sqrt[2 Pi] (-97692469875 + 34735100400 z - 8915961600 z^2 + 2612736000 z^3 - 1548288000 z^4 - 2972712960 z^5 - 3170893824 z^6 + 268435456 z^7) Erfi[Sqrt[2] z^(1/4)]))/E^(2 Sqrt[z])/(3298534883328 z^(19/4)))

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]