An Introduction to the Theory of Elliptic Functions and Higher Transcendentals

The Appendices and B are intended to add to the usefulness of the book as an introdluction to the theory of elliptic functions s►nd higher transcendentally, and it is earnestly hoped that the publication of this book may popularise the stndy of elliptic functions among advanced students of Higher lIftthke. [...] Table of the rep. e1E. -ientg the expos. n. ion of a Fs) 72 2, 'ulnas r. f the co- efE. ,:iont% in the expansion of in (s) . [...] Weisrsirossion sigma functions expressions of the theta functions of oriel variable in terms of the sigma functions ; expressions for the estanotione terms of the theta (auctions a P 77 2- Allottnal relations between the theta functions. [...] Although the Jacobian elliptic functions an, on, do are being, or have been, discarded in favour of the Weierstrassian %-function, the theta-functions still hold the field: According to Poincari, the simpli- city of the development of these series, the rapidity of their conver- gence, the elegance of their properties assure to them a place of impor- tanoe and from this place they cannot be dislodg [...] C is a constant, the b's form a complete system of the zeros, and the a's, form a complete Iiiyouna of the poles, of the function Az), and they are so chosen that bi +6. +. +b, 44, +a* +. +a ; thus if the zeros 13 and the poles u of f (:) ere assigned beforehand.