Chapter 12: Q6P (page 591)

To show $N_{(2 n + 1)} (x) = {(- 1)}^{n + 1} J_{- (2 n + 1)} (x)$ .

Short Answer

Expert verified

It is proved that $N_{(2 n + 1)} (x) = {(- 1)}^{n + 1} J_{- (2 n + 1)} (x)$

Step by step solution

Concept of Neumann Function:

The Neumann function:

$N_{p} (x) = \frac{c o s (πp) J_{p} (x) - J_{- p} (x)}{s i n (πp)}$

Calculation of the function N(n+12)(x) :

Consider the Neumann function as follows:

$N_{p} (x) = \frac{\cos (ττp) J_{p} (x) - J_{- p} (ττp)}{\sin (ττp)} N_{(n + \frac{1}{2})} (x) = \frac{\cos (n + \frac{1}{2}) (ττp) J_{_{(n + \frac{1}{2})}}^{(x) - J} - (n + \frac{1}{2})}{\sin (ττp) (n + \frac{1}{2})}$

$= \frac{\cos (nττ + \frac{ττ}{2}) J_{(n + \frac{1}{2})}^{(x) - J} - (n + \frac{1}{2})}{sinττ (n + \frac{1}{2})} = \frac{- J - {(n + \frac{1}{2})}^{(x)}}{{(- 1)}^{n}}$

Simplify further as follows:

$N_{(n + \frac{1}{2})} (x) = {(- 1)}^{(n + \frac{1}{2})} J_{(n + \frac{1}{2})} (x)$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

To show $N_{(2 n + 1)} (x) = {(- 1)}^{n + 1} J_{- (2 n + 1)} (x)$ .

Short Answer

Step by step solution

Concept of Neumann Function:

Calculation of the function N(n+12)(x) :

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Fields in Physics

Physics of Motion

Translational Dynamics

Magnetism and Electromagnetic Induction

Thermodynamics

Energy Physics

Study anywhere. Anytime. Across all devices.

To show N(2n+1)(x)=(-1)n+1J-2n+1(x).

Short Answer

Step by step solution

Concept of Neumann Function:

Calculation of the function N(n+12)(x) :

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Fields in Physics

Physics of Motion

Translational Dynamics

Magnetism and Electromagnetic Induction

Thermodynamics

Energy Physics

Study anywhere. Anytime. Across all devices.

To show $N_{(2 n + 1)} (x) = {(- 1)}^{n + 1} J_{- (2 n + 1)} (x)$ .