Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN: 9781133382119

Author: Swokowski

Publisher: Cengage

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Question

Hello. I need help with this question on Advanced Math topic. Thank you.

Expert Solution

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Step 1

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

**.**

*x**arrow_forward*

Step 2

Let us now multiply both sides by ** x**, in the above derivative of

**. After this we add the powers of two**

*J*_{n}**terms. This will help us change the power of**

*(x/2)***back to its original value.**

*(x/2)**arrow_forward*

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

**. In the second summation, we cancel out**

*J*_{n}**from numerator and denominator.**

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