Orthogonality limits of Bessel Polynomials

In summary, Bessel Polynomials are special functions that are solutions to Bessel's differential equation and are commonly used in physics and engineering. Orthogonality limits refer to the range of values over which the polynomials are orthogonal, and understanding these limits is important for accurate calculations and applications. The orthogonality limits are determined through mathematical analysis and have practical applications in signal processing, image reconstruction, and solving differential equations in physics and engineering.
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prhzn
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Anyone who knows the limits of orthogonality for Bessel polynomials? Been searching the Internet for a while now and I can't find a single source which explicitly states these limits (wiki, wolfram, articles, etc).

One thought: since the Bessel polynomials can be expressed as a generalized Laguerre polynomials, which have the orthogonality limits [tex][0,\infty)[/tex], would it be correct to assume that the Bessel polynomials inherits these limits?
 
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1. What are Bessel Polynomials?

Bessel Polynomials are a set of special functions that are solutions to Bessel's differential equation. They are named after the mathematician Friedrich Bessel and are commonly used in physics and engineering, particularly in the study of wave phenomena.

2. What do we mean by "orthogonality limits" in the context of Bessel Polynomials?

In mathematics, orthogonality refers to the concept of two mathematical objects being perpendicular or "at right angles" to each other. In the context of Bessel Polynomials, orthogonality limits refer to the range of values over which the polynomials are orthogonal, or perpendicular, to each other. This range is typically specified as a lower and upper limit.

3. Why is understanding the orthogonality limits of Bessel Polynomials important?

Understanding the orthogonality limits of Bessel Polynomials is important because it allows us to accurately use these functions in mathematical calculations and applications. By knowing the range of values over which the polynomials are orthogonal, we can ensure that our calculations are precise and reliable.

4. How are the orthogonality limits of Bessel Polynomials determined?

The orthogonality limits of Bessel Polynomials are determined through mathematical analysis and calculations. These calculations involve integrating the product of two Bessel Polynomials over a specified range of values, and the resulting value is used to determine the orthogonality limits.

5. Are there any practical applications of understanding the orthogonality limits of Bessel Polynomials?

Yes, there are many practical applications of understanding the orthogonality limits of Bessel Polynomials. These include using Bessel Polynomials in signal processing, image reconstruction, and solving differential equations in physics and engineering. By understanding the orthogonality limits, we can accurately use these functions in various fields of study and improve the accuracy of our calculations and models.

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