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Calculus / A First Course in Differential Equations with Modeling Applications 10 / Chapter 6.4 / Problem 21E

A First Course in Differential Equations with Modeling Applications | 10th Edition | ISBN: 9781111827052 | Authors: Dennis G. Zill

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Use the series in (7) to verify that is a real

Chapter 6, Problem 21E

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QUESTION:

Use the series in (7) to verify that \(I_{\nu}(x)=i^{-\nu} J_{\nu}(i x)\) is a real function.

Text Transcription:

I_nu(x)=i^-nu}J_nu(ix)

Questions & Answers

QUESTION:

Use the series in (7) to verify that \(I_{\nu}(x)=i^{-\nu} J_{\nu}(i x)\) is a real function.

Text Transcription:

I_nu(x)=i^-nu}J_nu(ix)

ANSWER:

Step 1 of 3

In this problem we have to prove that ${I}_{v}(x)={i}^{-v}{J}_{v}(ix)\$ is real

Where ${J}_{v}(x)=\sum\limits_{n=0}^{\infty{}}\frac{(-1{)}^{n}}{n!\ \Gamma{}(1+v+n)}(\frac{x}{2}{)}^{2n+v}$

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