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Math Help - Maple : Is it really that hard to realize that sin(pi)=0 ?!

  1. #1
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    Maple : Is it really that hard to realize that sin(pi)=0 ?!

    I have an annoying problem in Maple.

    I wanted maple to calculate the 10^th taylor series of f(x), while:

    f(x):=\frac{1}{2\pi}\int^{\pi}_0 e^{xcos(t)} dt

    and so I wrote :

    f := (int(exp(x*cos(t)), t = 0 .. pi))/(2*pi)
    p10 := taylor(f, x = 0, 11)

    And I got an answer that involved multiplying by sin(\pi). I must change all these into zeros, so I tried to use the 'subs' command, or to simplify, even 'simplify trig', but it didn't change a thing.

    What can I do in order to get a simple answer?

    Thank you
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  2. #2
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    The sine function is single-valued only in the Real world.

    Try forcing Maple to assume that 'x' is Real. You should be able to do this with a Symbolic Modifier.
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  3. #3
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    Oh... and how can I make Maple assume that 'x' is a real symbol?
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  4. #4
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    There should be an "Assume" paremeter. Something like (assume,x=real)
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  5. #5
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    You have to use Pi not pi, because pi is just a symbol, whereas Pi is the constant 3.14...

    Code:
    sin(Pi);
                                          0
    sin(pi);
                                       sin(pi)
    Code:
    f := (int(exp(x*cos(t)), t = 0 .. Pi))/(2*Pi);
                             int(exp(x cos(t)), t = 0 .. Pi)
                        f := -------------------------------
                                          2 Pi              
    p10 := taylor(f, x = 0, 11);
              1   1  2    1   4    1    6     1     8      1      10    / 11\
       p10 := - + - x  + --- x  + ---- x  + ------ x  + -------- x   + O\x  /
              2   8      128      4608      294912      29491200
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