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Title: Modified Bessel Function of the First Kind -- from Wolfram MathWorld

Open Graph Title: Modified Bessel Function of the First Kind -- from Wolfram MathWorld

X Title: Modified Bessel Function of the First Kind -- from Wolfram MathWorld

Description: A function I_n(x) which is one of the solutions to the modified Bessel differential equation and is closely related to the Bessel function of the first kind J_n(x). The above plot shows I_n(x) for n=1, 2, ..., 5. The modified Bessel function of the first kind is implemented in the Wolfram Language as BesselI[nu, z]. The modified Bessel function of the first kind I_n(z) can be defined by the contour integral I_n(z)=1/(2pii)∮e^((z/2)(t+1/t))t^(-n-1)dt, (1) where the contour encloses...

Open Graph Description: A function I_n(x) which is one of the solutions to the modified Bessel differential equation and is closely related to the Bessel function of the first kind J_n(x). The above plot shows I_n(x) for n=1, 2, ..., 5. The modified Bessel function of the first kind is implemented in the Wolfram Language as BesselI[nu, z]. The modified Bessel function of the first kind I_n(z) can be defined by the contour integral I_n(z)=1/(2pii)∮e^((z/2)(t+1/t))t^(-n-1)dt, (1) where the contour encloses...

X Description: A function I_n(x) which is one of the solutions to the modified Bessel differential equation and is closely related to the Bessel function of the first kind J_n(x). The above plot shows I_n(x) for n=1, 2, ..., 5. The modified Bessel function of the first kind is implemented in the Wolfram Language as BesselI[nu, z]. The modified Bessel function of the first kind I_n(z) can be defined by the contour integral I_n(z)=1/(2pii)∮e^((z/2)(t+1/t))t^(-n-1)dt, (1) where the contour encloses...

Opengraph URL: https://mathworld.wolfram.com/ModifiedBesselFunctionoftheFirstKind.html

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DC.TitleModified Bessel Function of the First Kind
DC.CreatorWeisstein, Eric W.
DC.DescriptionA function I_n(x) which is one of the solutions to the modified Bessel differential equation and is closely related to the Bessel function of the first kind J_n(x). The above plot shows I_n(x) for n=1, 2, ..., 5. The modified Bessel function of the first kind is implemented in the Wolfram Language as BesselI[nu, z]. The modified Bessel function of the first kind I_n(z) can be defined by the contour integral I_n(z)=1/(2pii)∮e^((z/2)(t+1/t))t^(-n-1)dt, (1) where the contour encloses...
DC.Date.Modified2004-08-05
DC.Subject33C10
DC.RightsCopyright 1999-2026 Wolfram Research, Inc. See https://mathworld.wolfram.com/about/terms.html for a full terms of use statement.
DC.Formattext/html
DC.Identifierhttps://mathworld.wolfram.com/ModifiedBesselFunctionoftheFirstKind.html
DC.Languageen
DC.PublisherWolfram Research, Inc.
DC.Relation.IsPartOfhttps://mathworld.wolfram.com/
DC.TypeText
Last-Modified2004-08-05
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