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21: Peter L. Walker

… ►was Professor of Mathematics at the American University of Sharjah, Sharjah, United Arab Emirates, in 1997–2005. He began his academic career in 1964 at the University of Lancaster, U. …Since 1984 he has also taught at other Persian Gulf universities, including Sultan Qaboos University, Oman. …

22: Charles W. Clark

… ►After a postdoctoral research associateship at Daresbury Laboratory in the U. … ►He has been a Visiting Fellow at the Australian National University, a Dr. Lee Fellow at Christ Church College of the University of Oxford, and Visiting Professor at the National University of Singapore. … ►He has served as Chair of the Division of Atomic, Molecular, and Optical Physics of the APS, Chair of the Physics Section of the AAAS, and as Program Manager for Atomic, Molecular, and Quantum Physics at the U. …

23: 26.17 The Twelvefold Way

… ►In this table

{\left(k\right)_{n}}

is Pochhammer’s symbol, and

S\left(n,k\right)

and

p_{k}\left(n\right)

are defined in §§26.8(i) and 26.9(i). … ►

Table 26.17.1: The twelvefold way.

► ►►►

elements of $N$	elements of $K$	$f$ unrestricted	$f$ one-to-one	$f$ onto
…
unlabeled	unlabeled	$p_{k}\left(n\right)$	$\begin{cases}1&n\leq k\\ 0&n>k\end{cases}$	$p_{k}\left(n\right)-p_{k-1}\left(n\right)$

►

24: Daniel W. Lozier

… ►He is currently a Research Associate at NIST and a General Editor for the DLMF project. … ►In 1963–1969 he worked at the U. … ►Lozier has been a frequent speaker at conferences, and has published numerous papers in journals and conference proceedings. …

25: 12.18 Methods of Computation

…

26: B. L. J. Braaksma

… ► 1934 in Groningen, The Netherlands) is Emeritus Professor in the Institute for Mathematics and Computer Science at the University of Groningen, The Netherlands. …

27: Simon Ruijsenaars

… ► 1948 in Hillegom, The Netherlands) is a Professor of Mathematical Physics at the University of Leeds. …

28: Funding

… ►Information about NSF Award 9980036 is available at NSF. …

29: 16.9 Zeros

… ►Then

{{}_{p}F_{p}}\left(\mathbf{a};\mathbf{b};z\right)

has at most finitely many zeros if and only if the

a_{j}

can be re-indexed for

j=1,\dots,p

in such a way that

a_{j}-b_{j}

is a nonnegative integer. … ►Then

{{}_{p}F_{p}}\left(\mathbf{a};\mathbf{b};z\right)

has at most finitely many real zeros. …

30: 31.18 Methods of Computation

… ►Subsequently, the coefficients in the necessary connection formulas can be calculated numerically by matching the values of solutions and their derivatives at suitably chosen values of

z

; see Laĭ (1994) and Lay et al. (1998). Care needs to be taken to choose integration paths in such a way that the wanted solution is growing in magnitude along the path at least as rapidly as all other solutions (§3.7(ii)). …