The logarithmic Choquard equation: sharp asymptotics and nondegeneracy of the groundstate (Q527390)

The authors derive the asymptotic decay of the unique positive, radially symmetric solution to the logarithmic Choquard equation in \(\mathbb R^2\), and established its nondegeneracy. Their proof relies on the multipole expansion of the logarithm kernel which is an identity related to the generating function of the Chebyshev polynomials and is also known as the cylindrical multipole expansion.