Question: How to convert series functions back to it original function

Good morning sirs,

Anyone with the idea(s) on how to convert series back to its original form should please share with me. 

Take for example

a-(1/2)*beta*a^2*y^2+(1/24)*beta^2*a^3*y^4-(1/720)*beta^3*a^4*y^6+(1/40320)*beta^4*a^5*y^8-(1/3628800)*beta^5*a^6*y^10+(1/479001600)*beta^6*a^7*y^12-(1/87178291200)*beta^7*a^8*y^14+O(y^16)

is a series for a*cos(sqr(a*beta)*y)

Thanking you in anticipation for your answer.

Please Wait...