دوال بيسيل

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This page is a translated version of the page Dictionary:Bessel functions and the translation is 10% complete.
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{{#category_index:B|Bessel functions}} دوال رياضية خاصة تستعمل في المسائل ذات التناظر الاسطواني، خاصة في المعادلات التي تربط عامل لابلاس لدالة بمشتقاتها. انظر Officer (1974, 52–55). سميت نسبة إلى عالم الرياضيات والفلك الألماني فريدريش ويليم بيسيل.


The Bessel ordinary differential equation

Bessel functions are particular solutions to the Bessel ordinary differential equation

Here need not be an integer and

Another form of this equation may be obtained by dividing through by the coefficient


One method of solution of this equation is to apply the Method of Frobenius, wherein a trial solution in the form of an infinite series

is substituted into the Bessel differential equation and the coefficients are found be equating terms of like powers in

The result of this procedure yields, in general, the series solution

Here is the Gamma Function being used as an analytic continuation of the factorial function.

For where is an integer, this reduces to


and this also holds for negative values of

Here .


External links

find literature about
Bessel functions/ar
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