Why Are the Results in My PDF Different from the Attached Paper?

[TheDestroyer]

Hi Guyz,

Why the results in the paper I've attached aren't like the results I got in my pdf?

Please look at the paper in the last line, the second term doesn't correspond to what I calculated, What i calculated is in the pdf file, is it wrong?

Why in my work there is exponential terms while it's not in the paper?

Thank you for reading

 

[Astronuc]

Expand the exponential in terms of an infinite series, and ignore higher order terms, e.g. 1/T² and higher, which one can do with reasonable accuracy for small arguments.

 

[TheDestroyer]

What you said might be correct if the terms are added, but they are subtracted, that means this will happen

e^x=1+x+0.5 x^2
e^-x=1-x+0.5 x^2

(e^x)-(e^-x)=(1+x+0.5 x^2)-(1-x+0.5 x^2)=((((2x))))

That means a linear term value will remain and must be multiplied in the term, Right? and this doesn't agree with the paper :(

Thank you anyway,

Any other ideas?

 

[Astronuc]

I believe if one uses the fact that e_i = -e_e = e, then the second term is multiplied by -1, and

e (e^x) - -e (e^-x) = e (1 + x + . . . ) + e (1 - x + . . .) = 2e (x), where

x = -e (\delta\phi) / T

and the expression becomes

-2 e² (\delta\phi) / T

as in the paper or text.

 

[TheDestroyer]

Mr. Astronuc, Can you please check what I've written in the PDF?

if we did as you said then there will be more items multplied in the term, can you tell me what's the problem in the PDF? why it's not like the paper if we expanded the exponential terms in series?

Thank you