Hertz contact

Dear all

I'm doing an analysis where i need to evaluate the contact area acoording to hertz theory.

I have a book which shows me every step, except for how to calculate two coefficients, and insteads gives me a table of calculated values. 

For the contact patch dimensions a and b, i get the expression

where i need to determine m and n. My book (A swedish book without ISBN) simply states that m and n are functions of theta,

and writes a large table with m and n for different angles