Abstract
Bessel functions are widely encountered in research and are essential components of introductory undergraduate courses on mathematical physics. Here, I present a result for the integral of a product of a Bessel function and an exponential, using the method of introducing parameters into the problem to generate some symmetries. I then present an overview of other techniques that use this idea of increasing the parameter or dimensional space in order to make a problem easier to solve.
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Acknowledgement
I encountered and worked on this problem while at the PULS group at the Friedrich-Alexander-University in Erlangen-Nuremberg in Germany. I am grateful to my co-workers there for helpful discussions. I also thank the anonymous reviewer for suggesting I expand the ambit of the article to discuss other techniques that involve increasing the dimensional or parameter space in integration problems.
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Jayant Pande is an Assistant Professor in Physics in the Department of Physical and Natural Sciences at FLAME University, Pune. His current research is on complex system physics and theoretical ecology.
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Pande, J. Proof of a Bessel Function Integral. Reson 27, 1411–1428 (2022). https://doi.org/10.1007/s12045-022-1434-y
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DOI: https://doi.org/10.1007/s12045-022-1434-y