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besselfunction

bessel function

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There are 14 letters in BESSELFUNCTION ( B³C³E¹F⁴I¹L¹N¹O¹S¹T¹U¹ )

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Definitions of bessel function in various dictionaries:

BESSEL FUNCTION - Bessel functions, first defined by the mathematician Daniel Bernoulli and then generalized by Friedrich Bessel, are the canonical solutions y(x) of B...

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Bessel function might refer to
Bessel functions, first defined by the mathematician Daniel Bernoulli and then generalized by Friedrich Bessel, are the canonical solutions y(x) of Bessel's differential equation* * * * * x * * 2 * * * * * * * d * * 2 * * * y * * * d * * x * * 2 * * * * * * + * x * * * * d * y * * * d * x * * * * + * * ( * * * x * * 2 * * * − * * α * * 2 * * * * ) * * y * = * 0 * * * {\displaystyle x^{2}{\frac {d^{2}y}{dx^{2}}}+x{\frac {dy}{dx}}+\left(x^{2}-\alpha ^{2}\right)y=0} * for an arbitrary complex number α, the order of the Bessel function. Although α and −α produce the same differential equation, it is conventional to define different Bessel functions for these two values in such a way that the Bessel functions are mostly smooth functions of α. * The most important cases are when α is an integer or half-integer. * Bessel functions for integer α are also known as cylinder functions or the cylindrical harmonics because they appear in the solution to Laplace's equation in cylindrical coordinates. Spherical Bessel functions with half-integer α are obtained when the Helmholtz equation is solved in spherical coordinates.

Bessel function might refer to

Bessel functions, first defined by the mathematician Daniel Bernoulli and then generalized by Friedrich Bessel, are the canonical solutions y(x) of Bessel's differential equation*
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* {\displaystyle x^{2}{\frac {d^{2}y}{dx^{2}}}+x{\frac {dy}{dx}}+\left(x^{2}-\alpha ^{2}\right)y=0}
* for an arbitrary complex number α, the order of the Bessel function. Although α and −α produce the same differential equation, it is conventional to define different Bessel functions for these two values in such a way that the Bessel functions are mostly smooth functions of α.
* The most important cases are when α is an integer or half-integer.
* Bessel functions for integer α are also known as cylinder functions or the cylindrical harmonics because they appear in the solution to Laplace's equation in cylindrical coordinates. Spherical Bessel functions with half-integer α are obtained when the Helmholtz equation is solved in spherical coordinates.

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besselfunction

bessel function

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There are 14 letters in BESSELFUNCTION ( B3C3E1F4I1L1N1O1S1T1U1 )

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Definitions of bessel function in various dictionaries:

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There are 14 letters in BESSELFUNCTION ( B³C³E¹F⁴I¹L¹N¹O¹S¹T¹U¹ )