In some problems where sine, cosine or Bessel functions are involved (e.g. (l), p. 35 et seq.), one has to satisfy certain initial conditions so that one obtains relations of the type

where t is a real parameter such that |t| < 1, and ±αn(n = 1, 2, …) are real simple zeros of an even or odd integral function f(z), being z = x + iy. An's are coefficients to be determined and, of course, ±ω is a real number that is not a zero of f(z).