Generalized hypergeometric function 2F3: Specific values (formula 07.26.03.0016)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]

Specific values

Specialized values

For fixed z and integer parameters

http://functions.wolfram.com/07.26.03.0016.01

Input Form

HypergeometricPFQ[{-n, -n - 1/2}, {3/2, -2 n - 3/2, -2 n - 1}, z] == ((2^(3/2 + 2 n) (2 + 2 n)!)/(Sqrt[Pi] (4 + 4 n)!)) z^(3/4 + n) (E^Sqrt[z] Pi BesselI[5/2 + 2 n, Sqrt[z]] + 2 BesselK[5/2 + 2 n, Sqrt[z]] Sinh[Sqrt[z]]) /; Element[n, Integers] && n > 0

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)

2001-10-29

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},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]