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QUESTION


Find the Taylor series for $\sinh z$ about $z=0.$



ANSWER


$f(z)=\sinh z$. Now $f(0)=0$, $f^{'}(o)=1$, $f^{''}(0)=1$ etc. so
by Taylor's Theorem $$\sinh z=z+{z^3\over 3!}+ {z^5\over
5!}+\cdots$$



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