coefficient polynomial regression

Question

In my mega project I want to find out coefficient of polynomial equation .The eq is

f(x)=(ax+b)summation of(ci(x*mod(lamda))^i where i from 0 to degree of equation.

In this equation x is difference between days for ex. 10days,20days ie. after purchasing of one product user purchase another product after 10 days or 20 days.& y means how much time this sequence of 10 days or 20 days comes in database ex. user purchase a product series(after purchasing a they purchase b so ab is one series) of 10 days for 5 times so y=5.
so for that polynomial equation has been used. lamda is the error in that sequence & I know value of x,y,lamda,i,a,b. & ci is coefficient of polynomial equation.I have large database for x & y & I want to find eq f(x).So anyone can help me how to find constant ci (i=0 to i=degree of eq).