26 citations · 144 across the 37 of their papers we have counts for
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Kontsevich-Zagier Integrals for Automorphic Green's Functions. I
Yajun Zhou
In the framework of Kontsevich-Zagier periods, we derive integral representations for weight- automorphic Green's functions invariant under modular transformations in $\varGamma…
On Some Integrals Over the Product of Three Legendre Functions
Yajun Zhou
The definite integrals $ \int_{-1}^1(1-x^2)^{(ν-1)/2}[P_ν(x)]^3\D x$, $ \int_{-1}^1(1-x^2)^{(ν-1)/2}[P_ν(x)]^2P_ν(-x)\D x$, $\int_{-1}^1x(1-x^2)^{(ν-1)/2}[P_{ν+1}(x)]^3\D x $ and $…
Spherical Couplings and Multiple Elliptic Integrals
Yajun Zhou
Various integrals over elliptic integrals are evaluated as couplings on spheres, resulting in some integral and series representations for the mathematical constants , and $…
A Simple Formula for Scalar Curvature of Level Sets in Euclidean Spaces
Yajun Zhou
A simple formula is derived for the Ricci scalar curvature of any smooth level set embedded in the Euclidean space , in terms of the grad…
Legendre Functions, Spherical Rotations, and Multiple Elliptic Integrals
Yajun Zhou
A closed-form formula is derived for the generalized Clebsch-Gordan integral $ \int_{-1}^1 {[}P_ν(x){]}^2P_ν(-x)\D x$, with being the Legendre function of arbitrary complex…