Friday, April 24, 2015

Some Useful Taylor Series Expansions

We frequently need these expansion for various calculations including making integration simpler.
For example, If we require to integrate tanx/x with respect to x, the job seems difficult.
But expanding tanx by Taylor series makes it simpler.
As, we know,
tanx= x+ (x^2)/2+(x^3)/3+(2x^5)/15+......
then tanx/x becomes 1+(x^2)/3+ (2x^4)/15+......
Though it's an approximation, we get a fairly good result by ignoring terms with higher order.
These expansions are credited to English mathematician Brook Taylor which along with the theorem named after him he is best known for.

Given below are some most used expansions:

Sources:
[2] Wikipedia: Brook Taylor

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