Identities involving elementary symmetric functions
نویسندگان
چکیده
منابع مشابه
Identities involving elementary symmetric functions
A systematic procedure for generating certain identities involving elementary symmetric functions is proposed. These identities, as particular cases, lead to new identities for binomial and q-binomial coefficients.
متن کاملCombinatorial Proofs of Identities Involving Symmetric Matrices
Brualdi and Ma found a connection between involutions of length n with k descents and symmetric k×k matrices with non-negative integer entries summing to n and having no row or column of zeros. From their main theorem they derived two alternating sums by algebraic means and asked for combinatorial proofs. The purpose of this note is to give such demonstrations.
متن کاملLocal Identities Involving Jacobi Elliptic Functions
We derive a number of local identities of arbitrary rank involving Jacobi elliptic functions and use them to obtain several new results. First, we present an alternative, simpler derivation of the cyclic identities discovered by us recently, along with an extension to several new cyclic identities of arbitrary rank. Second, we obtain a generalization to cyclic identities in which successive ter...
متن کاملCyclic Identities Involving Jacobi Elliptic Functions
We state and discuss numerous mathematical identities involving Jacobi elliptic functions sn (x,m), cn (x,m), dn (x,m), where m is the elliptic modulus parameter. In all identities, the arguments of the Jacobi functions are separated by either 2K(m)/p or 4K(m)/p, where p is an integer and K(m) is the complete elliptic integral of the first kind. Each p-point identity of rank r involves a cyclic...
متن کاملCyclic Identities Involving Jacobi Elliptic Functions. II
Abstract: Identities involving cyclic sums of terms composed from Jacobi elliptic functions evaluated at p equally shifted points on the real axis were recently found. These identities played a crucial role in discovering linear superposition solutions of a large number of important nonlinear equations. We derive four master identities, from which the identities discussed earlier are derivable ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and General
سال: 2000
ISSN: 0305-4470,1361-6447
DOI: 10.1088/0305-4470/33/29/101