An Elementary Treatise on Elliptic Functions (Classic Reprint)

The present treatise is founded upon Legendres TraiU desF onctions EU ipU ques, and upon Jacobi sF wndamenta Nova, and Memoirs by him inC relW sJ ournal: comparatively very little use is made of the investigations of A bel or of those of later authors. I show how the transition is made from Legendre sE lliptic Integrals of the three kinds to Jacobi sA mplitude, which is the argument of theE lliptic Functions (the sine, cosine, and delta of the amplitude, or as with Qudermann I write them, sn, en, dn), and also of Jacobi sfunctions Z, 11, which replace the integrals of the second and third kinds, and of the functions 0, H, which he was thence led to. It may be remarked as regards the Fundamenta Nova, that in the first part Jacobi (so to speak) hurries on to the problem of transformation without any suflB cient development of the theory of the elliptic functions themselves; and that in the concluding part, starting with the developments furnished by the transformationformulae, he connects with these, introducing them as the occasion arises, his new functions Z, 11, ,H: there are thus various points which require to be more fully discussed.
(Typographical errors above are due to OCR software and don't occur in the book.)

About the Publisher

Forgotten Books is a publisher of historical writings, such as: Philosophy, Classics, Science, Religion, History, Folklore and Mythology.

Forgotten Books' Classic Reprint Series utilizes the latest technology to regenerate facsimiles of historically important writings. Careful attention has been made to accurately preserve the original format of each page whilst digitally enhancing the aged text. Read books online for free at www.forgottenbooks.org