Generalized hypergeometric function 2F3: Specific values (formula 07.26.03.0017)

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/07.26.03.0017.01

Input Form

HypergeometricPFQ[{-(n/2), (1 - n)/2}, {1/2, -n, 1/2 - n}, z] == (2^(-(1/2) - n)/Gamma[1/2 + n]) z^((2 n + 1)/4) (((-1)^n Pi BesselI[1/2 + n, Sqrt[z]])/E^Sqrt[z] + 2 Cosh[Sqrt[z]] BesselK[1/2 + n, 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]