Two identities are obtained by Jacobi's triple product identity and some basic operators. By applying these identities, Jacobi's theorem for the number of representations of an integer as a sum of eight square...Two identities are obtained by Jacobi's triple product identity and some basic operators. By applying these identities, Jacobi's theorem for the number of representations of an integer as a sum of eight squares is easily proved.展开更多
In the ＂lost notebook＂, Ramanujan recorded infinite product expansions for where r -= r（q） is the Rogers-Ramanujan continued fraction. We shall give analogues of these results that involve Ramanujan＇s function k ...In the ＂lost notebook＂, Ramanujan recorded infinite product expansions for where r -= r（q） is the Rogers-Ramanujan continued fraction. We shall give analogues of these results that involve Ramanujan＇s function k = k（q） = r（q）r2 （q2）.展开更多
文摘Two identities are obtained by Jacobi's triple product identity and some basic operators. By applying these identities, Jacobi's theorem for the number of representations of an integer as a sum of eight squares is easily proved.
文摘In the ＂lost notebook＂, Ramanujan recorded infinite product expansions for where r -= r（q） is the Rogers-Ramanujan continued fraction. We shall give analogues of these results that involve Ramanujan＇s function k = k（q） = r（q）r2 （q2）.
