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11: Peter L. Walker

… ►, where he was a founding member. … ►Walker’s books are An Introduction to Complex Analysis, published by Hilger in 1974, The Theory of Fourier Series and Integrals, published by Wiley in 1986, Elliptic Functions. A Constructive Approach, published by Wiley in 1996, and Examples and Theorems in Analysis, published by Springer in 2004. He was also a contributor to the Wiley Handbook of Applicable Mathematics, published by Wiley in 1983. …

12: 18.32 OP’s with Respect to Freud Weights

§18.32 OP’s with Respect to Freud Weights

… ►where $Q(x)$ is real, even, nonnegative, and continuously differentiable, where $x{Q}^{\prime }(x)$ increases for $x>0$, and $Q^{\prime }(x)\to \mathrm{\infty }$ as $x\to \mathrm{\infty }$, see Freud (1969). … ►For asymptotic approximations to OP’s that correspond to Freud weights with more general functions $Q(x)$ see Deift et al. (1999a, b), Bleher and Its (1999), and Kriecherbauer and McLaughlin (1999). … ►All of these forms appear in applications, see §18.39(iii) and Table 18.39.1, albeit sometimes with $x\in [0,\mathrm{\infty })$, where the term half-Freud weight is used; or on $x\in [-1,1]$ or $[0,1]$, where the term Rys weight is employed, see Rys et al. (1983). …

13: Michael V. Berry

… ►, where he has been since 1965. … ►Berry was a member of the original editorial committee for the DLMF project, in existence from the mid-1990’s to the mid-2010’s. …

14: 13.27 Mathematical Applications

… ►where $\alpha$, $\beta$, $\gamma$, $\delta$ are real numbers, and $\gamma >0$. Vilenkin (1968, Chapter 8) constructs irreducible representations of this group, in which the diagonal matrices correspond to operators of multiplication by an exponential function. The other group elements correspond to integral operators whose kernels can be expressed in terms of Whittaker functions. This identification can be used to obtain various properties of the Whittaker functions, including recurrence relations and derivatives. … ►For applications of Whittaker functions to the uniform asymptotic theory of differential equations with a coalescing turning point and simple pole see §§2.8(vi) and 18.15(i). …

15: 27.21 Tables

… ►Lehmer (1914) lists all primes up to 100 06721. …Table II lists all solutions $n$ of the equation $f\left(n\right)=m$ for all $m\le 2500$, where $f\left(n\right)$ is defined by (27.14.2). … ►Those published prior to 1918 are mentioned in Dickson (1919). The bibliography in Lehmer (1941) gives references to the places in Dickson’s History where the older tables are cited. … ►No sequel to Lehmer (1941) exists to date, but many tables of functions of number theory are included in Unpublished Mathematical Tables (1944). …

16: Diego Dominici

… ►Diego was a Full Professor at the State University of New York at New Paltz where he was Department Chair for many years. … ►In 2008 Dominici received a Research Fellowship from the Alexander von Humboldt Foundation and visited the Technische Universität Berlin in Germany. …

17: 32.13 Reductions of Partial Differential Equations

… ►where $w(z)$ satisfies ${\text{P}}_{\text{II}}$ with $\alpha$ a constant of integration. … ►where $w(z)$ satisfies ${\text{P}}_{\text{II}}$. … ►where $\lambda$ is an arbitrary constant and $W(z)$ is expressible in terms of solutions of ${\text{P}}_{\text{I}}$. … ►where $v(z)$ satisfies (32.2.10) with $\alpha =\frac{1}{2}$ and $\gamma =0$. … ►where $c$ is an arbitrary constant and $v(z)$ satisfies …

18: 26.2 Basic Definitions

… ►A permutation is a one-to-one and onto function from a non-empty set to itself. If the set consists of the integers 1 through $n$, a permutation $\sigma$ can be thought of as a rearrangement of these integers where the integer in position $j$ is $\sigma (j)$. … ►Given a finite set $S$ with permutation $\sigma$, a cycle is an ordered equivalence class of elements of $S$ where $j$ is equivalent to $k$ if there exists an $\mathrm{\ell }=\mathrm{\ell }(j,k)$ such that $j={\sigma }^{\mathrm{\ell }}(k)$, where ${\sigma }^1=\sigma$ and ${\sigma }^{\mathrm{\ell }}$ is the composition of $\sigma$ with ${\sigma }^{\mathrm{\ell }-1}$. …The function $\sigma$ also interchanges 3 and 6, and sends 4 to itself. … ►The integers whose sum is $n$ are referred to as the parts in the partition. …

19: Daniel W. Lozier

… ►Then he transferred to NIST (then known as the National Bureau of Standards), where he collaborated for several years with the Building and Fire Research Laboratory developing and applying finite-difference and spectral methods to differential equation models of fire growth. …

20: Morris Newman

… ►In 1977 Newman became a professor at the University of California, Santa Barbara, where he served until his retirement in 1993. He continued to be technically active until his death in 2007, advising graduate students through early 2005. … ►Newman was a member of the original editorial committee for the DLMF project, in existence from the mid-1990’s to the mid-2010’s. …