Since the constant part of the right member of (28) has exactly the same period as the constant in the complementary function then non- periodic terms will
containing both cosine and sine terms as well as a constant. Thus an even function has no sine terms in its Fourier series.
and if the periodic function has a non-zero average value
Therefore to get interesting doubly-periodic functions
viously stated. Here aq+1(t) is an a. p. function which again has no constant term and whose least frequency is greater than (q + 1) y. Since the aj (t) are.
As in [1] the main difficulty to overcome was the definition and the the constant ones
when I q I = j r j = 1 the equation in general has no analytic solution. The periodic functions which may be defined in terms of two solutions of an.
4.1 Fourier Series for Periodic Functions. 319 include more terms. Away from the jumps we safely approach SW(x)=1or ?1. At x = ?/2
differential equation of the n-th order having simply periodic coefficients. In the terms not depending upon yu (at least in a large part of the ...
However since a periodic function has infinitely many (non- Note 7: The constant term in the Fourier series