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Given a positive nondecreasing sequence 0<lambda_1<=lambda_2<=..., the zeta-regularized product is defined by product_(n=1)^^^inftylambda_n=exp(-zeta_lambda^'(0)), where ...

Linear Algebra

Trigonometry

de Rham cohomology is a formal set-up for the analytic problem: If you have a differential k-form omega on a manifold M, is it the exterior derivative of another differential ...

When p is a prime number, then a p-group is a group, all of whose elements have order some power of p. For a finite group, the equivalent definition is that the number of ...

q-calculus or quantum calculus is a methodology comparable to the usual study of calculus but which is centered on the idea of deriving q-analogous results without the use of ...

A q-analog of the Chu-Vandermonde identity given by where _2phi_1(a,b;c;q,z) is the q-hypergeometric function. The identity can also be written as ...

A q-analog of the Saalschütz theorem due to Jackson is given by where _3phi_2 is the q-hypergeometric function (Koepf 1998, p. 40; Schilling and Warnaar 1999).

A number of interesting graphs are associated with the work of van Cleemput and Zamfirescu (2018). Two 13- and 15-node graphs, denoted alpha and beta respectively, were used ...

In the usual diagram of inclusion homomorphisms, if the upper two maps are injective, then so are the other two. More formally, consider a space X which is expressible as the ...