plz can someone help me to proof this

Jun 2016
1
0
italy
Dear all

I need your help I want to proov the follwing
Untitled.png

Thanks in advance
 

chiro

MHF Helper
Sep 2012
6,608
1,263
Australia
Hey majed.

Can you please show us what you have tried?
 
Dec 2013
2,002
757
Colombia
You should start by noticing that you have
\(\displaystyle \sum_{n=-J}^{J} \mathrm e^{nx \over J} = 1 + \sum_{n=1}^J \mathrm e^{-{nx \over J}} + \mathrm e^{nx \over J} = 1 + \sum_{n=1}^J 2\cosh{nx \over J}\)​
I would then multiply this by \(\displaystyle \sinh{x \over 2J}\) and use product-sum identities to simplify.

Why do so many people use such needlessly complicated notation on here? What is \(\displaystyle m_j\) all about?
 
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