For 𝛼, 𝛽 ∈ ℕ₀ and max{𝛼, 𝛽} > 0, it is shown that the integrals of the Jacobi polynomials∫0t(t−0) δPn(α12,β12)(cosθ)(sinθ2)2α(cosθ2)2βdθ>0for all 𝑡 ∈ (0, 𝜋] and 𝑛 ∈ ℕ if 𝛿 ≥ 𝛼 + 1 for 𝛼, 𝛽 ...

We consider solving integral equations on a piecewise smooth surface S in R3 with a smooth kernel function, using piecewise polynomial collocation interpolation of the surface. The theoretical ...

Multiple orthogonal polynomials (MOPs) extend the classical notion of orthogonality by satisfying simultaneous orthogonality conditions with respect to several weight functions or measures. This ...

The heart of DSP is, naturally enough, numbers. More specifically, DSP deals with how numbers are processed. Most texts on DSP either assume that the reader already has a background in numerical ...

Vesselin Dimitrov’s proof of the Schinzel-Zassenhaus conjecture quantifies the way special values of polynomials push each other apart. In the physical world, objects often push each other apart in an ...

How can the behavior of elementary particles and the structure of the entire universe be described using the same mathematical concepts? This question is at the heart of recent work by the ...

Long considered solved, David Hilbert’s question about seventh-degree polynomials is leading researchers to a new web of mathematical connections. Success is rare in math. Just ask Benson Farb. “The ...