The series of Fourier, Legendre, and Bessel, together with others, have a common field of application in connection with the solution of what are commonly called the “partial differential equations of mathematical physics.” One of the most important of these is*Laplace’s equation*, having for three independent variables the form

(1)

No less important is the corresponding equation in two independent variables,

(2)

to which (1) reduces either if a plane problem is under consideration instead of one in space, or if the functions Relating to a space problem are so specialized as to be independent of the

EP - 114 ET - 1 PB - Mathematical Association of America PY - 1941 SN - 9780883851357 SP - 91 T2 - Fourier Series and Orthogonal Polynomials UR - http://www.jstor.org/stable/10.4169/j.ctt5hh8cf.7 VL - 6 Y2 - 2021/09/25/ ER -