This is a preview. Log in through your library . Abstract In this paper we study strictly positive definite functions on the unit sphere of the m-dimensional Euclidean space. Such functions can be ...

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 ...

Positive definite matrices play a central role in mathematics, physics, statistics and engineering due to their unique properties and widespread applicability. These matrices, which are characterised ...