Find a Fourier series to represent the function exp(x) for x belongs to (-pi,pi) and hence derive pi/sinh(pi).

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Find a Fourier series to represent the function exp(x) for x belongs to $(-pi, pi)$ and hence derive $fracpisinh(pi)$.



Unable to derive the pi over sinh(pi) part...how do I do it?










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  • First: Use MathJax. Second, show us the Fourier series you got.
    – amsmath
    Sep 7 at 4:17










  • I do not know how to use mathjax.
    – Krishna Deshmukh
    Sep 7 at 7:44














up vote
0
down vote

favorite












Find a Fourier series to represent the function exp(x) for x belongs to $(-pi, pi)$ and hence derive $fracpisinh(pi)$.



Unable to derive the pi over sinh(pi) part...how do I do it?










share|cite|improve this question























  • First: Use MathJax. Second, show us the Fourier series you got.
    – amsmath
    Sep 7 at 4:17










  • I do not know how to use mathjax.
    – Krishna Deshmukh
    Sep 7 at 7:44












up vote
0
down vote

favorite









up vote
0
down vote

favorite











Find a Fourier series to represent the function exp(x) for x belongs to $(-pi, pi)$ and hence derive $fracpisinh(pi)$.



Unable to derive the pi over sinh(pi) part...how do I do it?










share|cite|improve this question















Find a Fourier series to represent the function exp(x) for x belongs to $(-pi, pi)$ and hence derive $fracpisinh(pi)$.



Unable to derive the pi over sinh(pi) part...how do I do it?







fourier-series






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edited Sep 9 at 7:41









MR ASSASSINS117

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asked Sep 7 at 4:13









Krishna Deshmukh

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146











  • First: Use MathJax. Second, show us the Fourier series you got.
    – amsmath
    Sep 7 at 4:17










  • I do not know how to use mathjax.
    – Krishna Deshmukh
    Sep 7 at 7:44
















  • First: Use MathJax. Second, show us the Fourier series you got.
    – amsmath
    Sep 7 at 4:17










  • I do not know how to use mathjax.
    – Krishna Deshmukh
    Sep 7 at 7:44















First: Use MathJax. Second, show us the Fourier series you got.
– amsmath
Sep 7 at 4:17




First: Use MathJax. Second, show us the Fourier series you got.
– amsmath
Sep 7 at 4:17












I do not know how to use mathjax.
– Krishna Deshmukh
Sep 7 at 7:44




I do not know how to use mathjax.
– Krishna Deshmukh
Sep 7 at 7:44










1 Answer
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Hint:
Find
$$a_0=dfrac1piint_-pi^pi e^x dx$$
$$a_n=dfrac1piint_-pi^pi e^xcos(nx) dx$$
$$b_n=dfrac1piint_-pi^pi e^xsin(nx) dx$$
then
$$S(f)(x)=frac12a_0+sum_n=1^inftya_ncos(nx)+b_nsin(nx)$$






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    1 Answer
    1






    active

    oldest

    votes








    1 Answer
    1






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes








    up vote
    0
    down vote













    Hint:
    Find
    $$a_0=dfrac1piint_-pi^pi e^x dx$$
    $$a_n=dfrac1piint_-pi^pi e^xcos(nx) dx$$
    $$b_n=dfrac1piint_-pi^pi e^xsin(nx) dx$$
    then
    $$S(f)(x)=frac12a_0+sum_n=1^inftya_ncos(nx)+b_nsin(nx)$$






    share|cite|improve this answer
























      up vote
      0
      down vote













      Hint:
      Find
      $$a_0=dfrac1piint_-pi^pi e^x dx$$
      $$a_n=dfrac1piint_-pi^pi e^xcos(nx) dx$$
      $$b_n=dfrac1piint_-pi^pi e^xsin(nx) dx$$
      then
      $$S(f)(x)=frac12a_0+sum_n=1^inftya_ncos(nx)+b_nsin(nx)$$






      share|cite|improve this answer






















        up vote
        0
        down vote










        up vote
        0
        down vote









        Hint:
        Find
        $$a_0=dfrac1piint_-pi^pi e^x dx$$
        $$a_n=dfrac1piint_-pi^pi e^xcos(nx) dx$$
        $$b_n=dfrac1piint_-pi^pi e^xsin(nx) dx$$
        then
        $$S(f)(x)=frac12a_0+sum_n=1^inftya_ncos(nx)+b_nsin(nx)$$






        share|cite|improve this answer












        Hint:
        Find
        $$a_0=dfrac1piint_-pi^pi e^x dx$$
        $$a_n=dfrac1piint_-pi^pi e^xcos(nx) dx$$
        $$b_n=dfrac1piint_-pi^pi e^xsin(nx) dx$$
        then
        $$S(f)(x)=frac12a_0+sum_n=1^inftya_ncos(nx)+b_nsin(nx)$$







        share|cite|improve this answer












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        share|cite|improve this answer










        answered Sep 7 at 5:07









        Nosrati

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