Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8290)

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`=3/2

http://functions.wolfram.com/07.22.03.8290.01

Input Form

HypergeometricPFQ[{-(23/4)}, {3/2, -(15/4)}, z] == (1/(72364792500 Sqrt[z])) ((-15058768725 + 15058768725 E^(4 Sqrt[z]) + 6064858800 Sqrt[z] + 6064858800 E^(4 Sqrt[z]) Sqrt[z] - 2043241200 z + 2043241200 E^(4 Sqrt[z]) z + 691891200 z^(3/2) + 691891200 E^(4 Sqrt[z]) z^(3/2) - 252806400 z^2 + 252806400 E^(4 Sqrt[z]) z^2 + 104509440 z^(5/2) + 104509440 E^(4 Sqrt[z]) z^(5/2) - 51179520 z^3 + 51179520 E^(4 Sqrt[z]) z^3 + 31457280 z^(7/2) + 31457280 E^(4 Sqrt[z]) z^(7/2) - 26542080 z^4 + 26542080 E^(4 Sqrt[z]) z^4 + 36700160 z^(9/2) + 36700160 E^(4 Sqrt[z]) z^(9/2) - 149946368 z^5 + 149946368 E^(4 Sqrt[z]) z^5 - 1048576 z^(11/2) - 1048576 E^(4 Sqrt[z]) z^(11/2) + 4194304 z^6 - 4194304 E^(4 Sqrt[z]) z^6 + 262144 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(21/4) (-575 + 16 z) Erf[Sqrt[2] z^(1/4)] + 262144 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(21/4) (-575 + 16 z) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z]))

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]