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Given two univariate polynomials of the same order whose first p coefficients (but not the first p-1) are 0 where the coefficients of the second approach the corresponding ...

A formula for the generalized Catalan number _pd_(qi). The general formula is (n-q; k-1)=sum_(i=1)^k_pd_(qi)(n-pi; k-i), where (n; k) is a binomial coefficient, although ...

The numbers B_(n,k)(1!,2!,3!,...)=(n-1; k-1)(n!)/(k!), where B_(n,k) is a Bell polynomial.

For all integers n and |x|<a, lambda_n^((t))(x+a)=sum_(k=0)^infty|_n; k]lambda_(n-k)^((t))(a)x^k, where lambda_n^((t)) is the harmonic logarithm and |_n; k] is a Roman ...

Each subsequent row of Pascal's triangle is obtained by adding the two entries diagonally above. This follows immediately from the binomial coefficient identity (n; r) = ...

sum_(k=-infty)^infty(a; m-k)(b; n-k)(a+b+k; k)=(a+n; m)(b+m; n).

Let (K,|·|) be a complete non-Archimedean valuated field, with valuation ring R, and let f(X) be a power series with coefficients in R. Suppose at least one of the ...

A q-analog of the multinomial coefficient, defined as ([a_1+...+a_n]_q!)/([a_1]_q!...[a_n]_q!), where [n]_q! is a q-factorial.

The system of partial differential equations iu_t+u_(xx)+alphau_(yy)+betau|u|^2-uv=0 v_(xx)+gammav_(yy)+delta(|u|^2)_(yy)=0.

The system of partial differential equations u_t = u_(xx)+u(u-a)(1-u)+w (1) w_t = epsilonu. (2)