The 163 appearing here is the same one appearing in the fact that (the Ramanujan constant) is very nearly an integer. Similarly, the factor comes from the j-function identity for . The series is given by (86) (87) (Borwein and Borwein 1993; Beck and Trott; Bailey et al. 2007,...
The proof of the main result illustrates Hilbert's Theorem 90. An example of a particular formula generalizing Ramanujan's formulas for degree 5 is given. A necessary condition for nested radical expressions of depth 2 to be contained in the normal closure of a pure cubic extension of the ...
For example, we show that the coefficients af(n),n≥1, of Ramanujan's mock theta function(1)f(q)=1+∑n=1∞qn2(1+q)2(1+q2)2⋯(1+qn)2=1+∑n=1∞af(n)qn are given byaf(n)=−124n−1ℑ(∑Q∈QnF(zQ)ωQ), where(2)F(z)=−140⋅E4(z)+4E4(2z)−9E4(...
In [13] Ramanujan introduced the following trigonometrical sum. Definition 1.1. The Ramanujan sum is defined by c q (n) =(h,q)=1 e 2πinh/q , (1.1) where q and n are in N and the summation is over a reduced residue system mod q. ...
New infinite families of exact sums of squares formulas,Jacobi elliptic functions,and Ramanujan’staufunction and 24 squares identities were originally obtained via multiple basic hypergeometric series,Gustafson’s C nonterminating 65 summation theorem,and Andrews’ ... S Milne - 《Proc Natl Acad Sci...
In this thesis, by making use of different methods, many new Rogers-Ramanujan type identities andq-series transformation formulaehave been established. 本文用不同的方法得到了很多新的Rogers-Ramanujan型恒等式以及一些新的q-级数变换公式。 更多例句>> ...
while the Riemann-Christo,el tensor,eld and the Ricci tensor,eld are given by R(X(Y)Z,W)=g(R(X,Y)Z,W), ρ(X,Y)=trace(Z→R(X,Z)Y), where X(Y)Z,W are smooth vector,elds on H3.Moreover we put,as in[PS] or [S] , ...
As a byproduct we obtain an explicit parameterization of the affine Weyl group of $\\\hat{sl}_l$ by a simple combinatorial set.doi:10.1023/B:RAMA.0000012431.06614.0eFeigin, B.Jimbo, M.Loktev, S.Miwa, T.Mukhin, E.Springer NatureThe Ramanujan JournalB...
S. Yakubovich, A general class of Voronoi's and Koshliakov-Ramanujan's summation formulas involving dk(n), Integ. Trans. Spec. Func. 22 (2011), 801-821.Yakubovich S. A general class of Voronoi's and Koshliakov-Ramanujan's summation formulas involving dk(n). Integral Transforms Spec ...
Ramanujan J. 30(3) 341-378. MR3033681M. Josuat-Verg`es and J. S. Kim. Touchard-Riordan formulas, T-fractions, and Jacobi's triple product identity. to appear in Ramanujan Journal. http://arxiv.org/abs/1101.5608.Touchard-Riordan formulas, T-fractions, and Jacobi’s triple product ...