Generalized hypergeometric function 2F3: Specific values (formula 07.26.03.0014)

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/07.26.03.0014.01

Input Form

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