The Plancherel–Rotach asymptotics are asymptotic results for orthogonal polynomials. They are named after the Swiss mathematicians Michel Plancherel and...

}{2}}\right)\left(1-{\frac {x^{2}}{2n+1}}\right)^{-{\frac {1}{4}}}.} The Plancherel–Rotach asymptotics method, applied to Hermite polynomials, takes into account the...

} and ω {\displaystyle \omega } be positive and fixed. The Plancherel–Rotach asymptotics formulas: for x = ν cos 2 ⁡ φ {\displaystyle x=\nu \cos ^{2}\varphi...

measure Sheffer sequence Sturm–Liouville theory Umbral calculus Plancherel–Rotach asymptotics Demo of orthonormal polynomials obtained for different weight...

Analysis and Applications, 125: 58–71, doi:10.1016/0022-247x(87)90164-8 Zhang, R. (2006), "Plancherel-Rotach Asymptotics for q-Series", arXiv:math/0612216...