Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8mw)

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=-13/4, b_1`>=-11/2

For fixed z and a₁=-13/4, b_1`=3/2

http://functions.wolfram.com/07.22.03.a8mw.01

Input Form

HypergeometricPFQ[{-(13/4)}, {3/2, 7/4}, z] == (1/(113541120 z^(3/4))) ((-4 z^(1/4) (1567215 - 9706860 Sqrt[z] - 1681200 z + 7270080 z^(3/2) + 195840 z^2 - 795648 z^(5/2) - 4096 z^3 + 16384 z^(7/2) + E^(4 Sqrt[z]) (-1567215 - 9706860 Sqrt[z] + 1681200 z + 7270080 z^(3/2) - 195840 z^2 - 795648 z^(5/2) + 4096 z^3 + 16384 z^(7/2))) - E^(2 Sqrt[z]) Sqrt[2 Pi] (2027025 - 43243200 z + 29652480 z^2 - 3194880 z^3 + 65536 z^4) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] (2027025 - 43243200 z + 29652480 z^2 - 3194880 z^3 + 65536 z^4) 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]