IV. On certain linear differential equations of astronomical interest

Abstract

Part II. of the present paper was written, very much in the form in which it is now presented, in the summer of 1913, and began with the remark in 11, which appears to disprove a statement made by Poincaré in regard to the convergence of an astronomical series. It was laid aside partly because a good deal of the work is only of the nature of elementary algebra, partly because the matrix notation employed does not seem to find favour in its application to differential equations. Various circumstances have, however, led me to take up the matter again, and my original conviction that the method of Part II. is of importance has been strengthened by comparing it with the less formal methods which, for the sake of introducing the subject, I have followed in Part I. I hope, therefore, that the following exposition may be thought worth while. Part III. has only the value of a concluding remark. The table of contents above may serve to give an idea of the scope and arrangement of the paper.