continuous q-Hermite polynomials
♦ 4 matching pages ♦
4 matching pages
§18.28(vii) Continuous -Hermite Polynomials►
18.28.18►For continuous -Hermite polynomials the orthogonality measure is not unique. …
… ►For a uniform asymptotic expansion of the Stieltjes–Wigert polynomials, see Wang and Wong (2006). ►For asymptotic approximations to the largest zeros of the -Laguerre and continuous -Hermite polynomials see Chen and Ismail (1998).
4: 28.9 Zeros
… ►For real each of the functions , , , and has exactly zeros in . They are continuous in . For the zeros of and approach asymptotically the zeros of , and the zeros of and approach asymptotically the zeros of . Here denotes the Hermite polynomial of degree (§18.3). Furthermore, for and also have purely imaginary zeros that correspond uniquely to the purely imaginary -zeros of (§10.21(i)), and they are asymptotically equal as and . …