An Elementary Treatise on Series Spherical (Classic Reprint)

Trigonometric Series, following closely the treatment of that subject in Riemann sP artielle Differentialgleichungen, to accompany a short course on The Potential Function, given by Professor B. 0. Peirce. My course has been gradually modified and extended until it has become an introduction to Spherical Harmonics and Bessel sand Lame sF unctions. Two years ago my lecture notes were lithographed by my class for their ownuse and were found so convenient that I have prepared them for publication, hoping that they may prove useful to others as well as to my own students. Meanwhile, Professor Peirce has published his lectures on The Newtonian Potential Function (B oston, Ginn Co.), and the two sets of lectures form a course (M ath. 10) given regularly at Harvard, and intended as a partial introduction to modern Mathematical Physics. Students taking this course are supposed to be familiar with so much of the infinitesimal calculus as is contained in my Differential Calculus (B oston, Ginn Co.) and my Integral Calculus (second edition, same publishers), to which I refer in the present book as Dif. Cal. and I nt. Gal. Here, as in the Calculus, I speak of a derivative rather than a differential coefficient, and use the notation Dx instead of rfor partial derivative with ox respect to x. The course was at first, as I have said, an exposition of Riemann sP artielle Differentialgleichungen. In extending it, I drew largely from Ferrer sS pherical Harmonics and Heine sK ugelfunctionen, and was somewhat indebted toT odhunter (F unctions of Laplace, Bessel, and Lame- ), Lord Rayleigh (T heory of Sound ), andF orsyth (D ifferential Equations ). In preparing the notes for publication, I have been greatly aided by the criticisms and suggestions of my colleagues, Professor B. 0. Peirce and Dr. Maxime Bocher, and the latter has kindly contributed the brief historical sketch con
(Typographical errors above are due to OCR software and don't occur in the book.)