Bessel function transformation and also cos variation

AI Thread Summary
The discussion centers on the transformation of exponential functions to Bessel functions and the handling of cosine terms in the equations. The first question addresses the disappearance of the cosine term when setting n=1 and n=-1, specifically in relation to the equation equating to -wmt-pi/2. The second question seeks clarification on the method used to transform the exponential function into a Bessel function. Concerns are raised about the accuracy of equation 2, suggesting that the cosine should not appear in the exponent and can be expressed as a sum of exponential functions. The conversation highlights the need for precision in mathematical transformations and the interpretation of equations.
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Homework Statement


In a article I have found this transformation (exp to bessel function) . I have two questions.
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Homework Equations

The Attempt at a Solution



a)where did the Cos go after setting n=1 and n=-1 ? in the third equations ( it is equal to -wmt-pi/2)? why?)
b)how did the writer transform the exp to bessel function?

Thanks[/B]
 
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