Researches on the Multiplication of Elliptic Functions (Classic Reprint) - Couverture souple

Fujisawa, Rikitaro

Couverture souple

ISBN 10 : 1333670923 ISBN 13 : 9781333670924

Editeur : Forgotten Books, 2019

Synopsis

The digital edition of all books may be viewed on our website before purchase. Excerpt from Researches on the Multiplication of Elliptic Functions



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A propos du livre

Présentation de l'éditeur

Jacobi fidds la lor (jeneml dc la composition dc ces expressions est aisee a saisir, iiiid lurther remarks that we sluill have aiialoo-ous forinuliu by using, instead of tlie differential coefficients of A and B, those of :in(l Vj= (l-a-2xl-AV jAI -J--)( 1- .V )- X- The general form of tliese expressions is, however, by no mejins easy to infer from the ])aiticular cases just given, and I have tried to tnice among the writings of Jacobi, the steps which might liave led him to these expressions, but without success. The present memoir is divided into two ])art8. In the first ])art, the multiplication-formulie of elliptic functions are derived from A lxil stheorem for the elliptic integral of the first kind. It will be seen that one of the results arrived at is the general formula in question. It appears, however, highly improbable that Jacobi obtained his formula? in this way. In the }a|)er just alluded to, Jacobi gives, also without demonstration, the partial differential equation satisfied by the numerators and denominator of the multijjlication-formula?. This partial differential eiuation has since been obtained by 15etti, Cayley, I riot et Bou(|uet,f and others ;but the final results to be obtained by applying it to the actual evaluation of the numerical constants involved in the multiplication-formula?, has not, to my knowledge, hitherto been develoD ed with much completeness or success. In the second part, Jacobi spartial differential equation is derived in a manner which is most probably the one followed by Jacobi Betti, A nnali diM ateniatica, Vol. IV, p. 32. Cayley, Cambridge and Dublin Mathematical Journal, Vol. II, pp. 256-26C. tB riot et Bouquet, Theorie desF onctions Elliptiques, p. 529.
(Typographical errors above are due to OCR software and don't occur in the book.)

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Détails de l'édition

• Éditeur: Forgotten Books
• Date d'édition: 2019
• Langue: anglais
• ISBN 10: 1333670923
• ISBN 13: 9781333670924
• Reliure: Broché
• Nombre de pages: 80
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