Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.6802)

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=3, b₁>=-23/4

For fixed z and a₁=3, b₁=-23/4

http://functions.wolfram.com/07.22.03.6802.01

Input Form

HypergeometricPFQ[{3}, {-(23/4), 11/4}, z] == (1/(4614720 z^(7/4))) ((16 E^(2 Sqrt[z]) z^(3/4) (-2027025 - 741180 z + 54720 z^2 + 24576 z^3 + 512 z^4) + E^(4 Sqrt[z]) Sqrt[2 Pi] (-6081075 + 12162150 Sqrt[z] - 13513500 z + 10810800 z^(3/2) - 5821200 z^2 + 1552320 z^(5/2) + 282240 z^3 - 437760 z^(7/2) + 185600 z^4 - 40960 z^(9/2) + 4096 z^5) Erf[Sqrt[2] z^(1/4)] + Sqrt[2 Pi] (6081075 + 12162150 Sqrt[z] + 13513500 z + 10810800 z^(3/2) + 5821200 z^2 + 1552320 z^(5/2) - 282240 z^3 - 437760 z^(7/2) - 185600 z^4 - 40960 z^(9/2) - 4096 z^5) 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]