The Summation of the Integral Conjugate to the Fourier Integral of the Finite Type and Of the Conjugate Series

The integral conjugate to the Denjoy-Fourier Integral of the finite type [7] is

∫(b_s cos sx-a_s sin sx)ds,                                               (1)

where

a_s = 1/π∫f(t) cos st dt, b_s = 1/π∫f(t) sin st dt,                  (2)

and f (x) is supposed to be integrable-D in (-π, π) and to be zero outside this interval.