Ordinary Differential Equation


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Find the Taylor series of the following functions about x0 = 0. 

sinh(x)

May 18th, 2015

The Taylor series is: x + (x^3)/3! + (x^5)/5! + (x^8)/8! = ....

In terms of sigma notation it is: sigma(x^(2k+1)/(2k+1)!) as k goes from 0 to infinity.

To figure it out, recall that sinh(x) = (exp(​x)-​exp(​‑x))/​2, so you can 

get the series for exp(x) and the series for exp(-x), subtract the latter from the former, then divide by 2. If this isn't detailed enough, let me know.

May 18th, 2015

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May 18th, 2015
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May 18th, 2015
Nov 23rd, 2017
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