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Mathematics

4 posts

Notes on mathematical methods, identities, special functions, tensor calculus, Fourier analysis, and related foundations used throughout the site.

MathematicsGaussian Integrals and Related Fourier–Bessel Identities

We collect closed-form formulas for one- and \(n\)-dimensional Gaussian integrals with linear and oscillatory terms, derive even-moment integrals, and list several useful…

2025-01-29

MathematicsGamma, Polygamma, Hurwitz Zeta, and Bessel Function Identities

We collect a few basic identities for the gamma and polygamma functions, their link to the Hurwitz zeta function, standard asymptotics for Bessel functions, and a useful Bessel…

2024-06-29

MathematicsDyadic Products, Tensor Operations, and Surface Geometry in Euclidean Space

We collect working formulas for dyadic (outer) products, the double-dot contraction of tensors, and tensor–vector cross products expressed with the Levi-Civita symbol, and we…

2024-04-30

MathematicsLevi-Civita Symbol, Cross and Wedge Products, Hodge Star, and Metric Components

We review the Levi-Civita symbol in arbitrary dimension, its role in defining the cross product and wedge product, introduce the Hodge star on differential forms, and clarify…

2024-04-29