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11: Frank W. J. Olver

… ►Olver joined NIST in 1961 after having been recruited by Milton Abramowitz to be the author of the Chapter “Bessel Functions of Integer Order” in the Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, a publication which went on to become the most widely distributed and most highly cited publication in NIST’s history. … ►In April 2011, NIST co-organized a conference on “Special Functions in the 21st Century: Theory & Application” which was dedicated to Olver. …

12: 12.14 The Function $W(a,x)$

… ►In other cases the general theory of (12.2.2) is available. … ►

§12.14(iii) Graphs

… ►For graphs of the modulus functions see §12.14(iii). …

13: 22.19 Physical Applications

… ►Figure 22.19.1 shows the nature of the solutions $\theta (t)$ of (22.19.3) by graphing $\mathrm{am}(x,k)$ for both $0\le k\le 1$, as in Figure 22.16.1, and $k\ge 1$, where it is periodic. … ►plays a prototypal role in classical mechanics (Lawden (1989, §5.2)), quantum mechanics (Schulman (1981, Chapter 29)), and quantum field theory (Pokorski (1987, p. 203), Parisi (1988, §14.6)). Its dynamics for purely imaginary time is connected to the theory of instantons (Itzykson and Zuber (1980, p. 572), Schäfer and Shuryak (1998)), to WKB theory, and to large-order perturbation theory (Bender and Wu (1973), Simon (1982)). …

14: 10.74 Methods of Computation

… ►And since there are no error terms they could, in theory, be used for all values of $z$; however, there may be severe cancellation when $|z|$ is not large compared with $n^2$. … ►Methods for obtaining initial approximations to the zeros include asymptotic expansions (§§10.21(vi)-10.21(ix)), graphical intersection of $2D$ graphs in $ℝ$ (e. …