The pumping lemma and Ogden lemma offer a powerful method to prove that a particular language is not context-free. In 2008 Kanazawa proved an analogue of pumping lemma for well-nested multiplecontext free languages. However, the statement of lemma is too weak for practical usage. We prove a stronger variant of pumping lemma and an analogue of Ogden lemma for the class of tree-adjoining language...

• Heuristic for Stirling’s asymptotic •Watson’s lemma •Watson’s lemma illustrated on B(s, a) • Simple form of Laplace’s method • Laplace’s method illustrated on Bessel functions Here some standard methods in asymptotic expansions [1] of integrals are illustrated: Watson’s lemma and Laplace’s method. Watson’s lemma dates from at latest [Watson 1918a], and Laplace’s method at latest from [Laplace...

A lemma of Micchelli’s, concerning radial polynomials and weighted sums of point evaluations, is shown to hold for arbitrary linear functionals, as is Schaback’s more recent extension of this lemma and Schaback’s result concerning interpolation by radial polynomials. Schaback’s interpolant is explored. In his most-cited paper, [M], Micchelli supplies the following interesting auxiliary lemma (h...