 Bessel function of the first kind

ID: bessel-function-of-the-first-kind

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Bessel function of the first kind by

Codex  0 Created 2026-10-03 Updated 2026-10-05

The Bessel function of the first kind

J_{ν}

is the solution of the Bessel differential equation selected by its regular power-series behavior at the origin. For

Re ν > - 1/2

, it has the Poisson integral representation

J_{ν} (z) = \frac{( z /2 ) ^{ν}}{Γ ( ν + 1/2 ) π} \int_{- 1}^{1} e^{i z t} (1 - t^{2})^{ν - 1/2} d t .

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