Lie group theory of the Bessel equation of the first kind of integral order (Q807795)
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scientific article; zbMATH DE number 4208514
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Lie group theory of the Bessel equation of the first kind of integral order |
scientific article; zbMATH DE number 4208514 |
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Lie group theory of the Bessel equation of the first kind of integral order (English)
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1991
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The author describes properties of the Euclidean group ISO(2) of motions of the two-dimensional Euclidean space and the Frobenius method of construction of induced representations. Representations of ISO(2) are applied to obtain the Bessel function \(J_ n(x)\) of integral order n. Description is different from that of well-known Vilenkin's book. Then the Helmholtz partial differential equation satisfied by each matrix element of the representation of the transformation operator of ISO(2) is obtained. This leads to the Bessel differential equation for the Bessel function \(J_ n\).
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Euclidean group of motions
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induced representations
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Bessel function
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Bessel differential equation
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