Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Statements and Logic
Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.
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Hello. I need help with this question on Advanced Math topic. Thank you.

Hello. I need help with this question on Advanced Math topic. Thank you. Prove the following recurrence equations related to Bessel functions.
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Transcribed Image Text:Hello. I need help with this question on Advanced Math topic. Thank you. Prove the following recurrence equations related to Bessel functions.
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Step 1

We first consider the definition of Bessel function of order n and differentiate it w.r.t. x.

Advanced Math homework question answer, Step 1, Image 1
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Step 2

Let us now multiply both sides by x, in the above derivative of Jn. After this we add the powers of two (x/2) terms. This will help us change the power of (x/2) back to its original value.

Advanced Math homework question answer, Step 2, Image 1
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Step 3

Next, we split the summation in to two parts by opening the brackets of the term (n + 2r). By doing this, we observe that the first summation is the definition of Jn. In the second summation, we cancel out r from numerator and denominator.

Advanced Math homework question answer, Step 3, Image 1
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