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Bessel functions are solutions of "Bessel's differential equation" |
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Bessel functions, named after Friedrich Bessel, are solutions y(x) of "Bessel's differential equation" |
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:x2y'' + xy' + (x2 - n2)y = 0 |
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:x2y'' + xy' + (x2 - n2)y = 0 |
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for non-negative integer values of n. |
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for non-negative integer values of n. |
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* Bessel functions of the first kind * Bessel functions of the second kind |
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* Bessel functions of the first kind Jn(x), the solutions of the above differential equation which are defined for x = 0. * Bessel functions of the second kind Yn(x), the solutions which are non-singular (infinite) for x = 0. |
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They are important in many physical problems inclding those involving spherical or cylindrical? coordinates, and in frequency modulation. |
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The graphs of Bessel function look like oscillating sine or cosine functions which "level off" because they have been divided by a term of the order of √x. |
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Examples: * the solution to Schrodingers equation for the Hydrogen atom. |
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They are important in many physical problems including those involving spherical or cylindrical? coordinates, and in frequency modulation. Applications: * the solution to Schrödinger's equation for the Hydrogen atom. |
for non-negative integer values of n.
They come in two kinds:
The graphs of Bessel function look like oscillating sine or cosine functions which "level off" because they have been divided by a term of the order of √x.
They are important in many physical problems including those involving spherical or cylindrical? coordinates, and in frequency modulation.
Applications:
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