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1: Gergő Nemes

… … ► 1988 in Szeged, Hungary) is a Research Fellow at the Alfréd Rényi Institute of Mathematics in Budapest, Hungary. … ►As of September 20, 2021, Nemes performed a complete analysis and acted as main consultant for the update of the source citation and proof metadata for every formula in Chapter 25 Zeta and Related Functions. …

2: 20 Theta Functions

Chapter 20 Theta Functions

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3: William P. Reinhardt

… ►His undergraduate and graduate degrees are from the University of California at Berkeley and Harvard University, respectively. …Reinhardt is a frequent visitor to the NIST Physics Laboratory in Gaithersburg, and to the Joint Quantum Institute (JQI) and Institute for Physical Sciences and Technology (ISTP) at the University of Maryland. … ►Reinhardt was elected to Fellowship in: The American Physical Society 1980, the American Association for the Advancement of Science 1983, Phi Beta Kappa 1998, and The Institute of Physics (UK) 2000. … ►

20 Theta Functions

… ►In November 2015, Reinhardt was named Senior Associate Editor of the DLMF and Associate Editor for Chapters 20, 22, and 23.

4: Foreword

… ►In 1964 the National Institute of Standards and Technology published the Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, edited by Milton Abramowitz and Irene A. …That 1046-page tome proved to be an invaluable reference for the many scientists and engineers who use the special functions of applied mathematics in their day-to-day work, so much so that it became the most widely distributed and most highly cited NIST publication in the first 100 years of the institution’s existence. … ►However, we have also seen the birth of a new age of computing technology, which has not only changed how we utilize special functions, but also how we communicate technical information. … ►Particular attention is called to the generous support of the National Science Foundation, which made possible the participation of experts from academia and research institutes worldwide. … ►November 20, 2009 …

5: Tom M. Apostol

… … ► 2016) was Professor Emeritus in the Department of Mathematics at the California Institute of Technology (Caltech), Pasadena, California, until his death on May 8, 2016. … ►Apostol was born on August 20, 1923. He received his bachelor of science in chemical engineering in 1944 and a master’s degree in mathematics in 1946, both from the University of Washington, Seattle. … ►In 1982, Apostol received an award for teaching excellence from the Associated Students of the California Institute of Technology. …

6: Staff

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Tom M. Apostol, California Institute of Technology, Chaps. 25, 27

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William P. Reinhardt, University of Washington, Chaps. 20, 22, 23

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Peter L. Walker, American University of Sharjah, Chaps. 20, 22, 23

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William P. Reinhardt, University of Washington, for Chaps. 20, 22, 23

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Peter L. Walker, American University of Sharjah, for Chaps. 20, 22, 23

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7: Publications

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Toward a Revised NBS Handbook of Mathematical Functions, Technical Report NISTIR 6072 (September 1997), National Institute of Standards and Technology.

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Using Numerical Grid Generation to Facilitate 3D Visualization of Complicated Mathematical Functions, Technical Report NISTIR 6413 (November 1999), National Institute of Standards and Technology.

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Interactive 3D Visualization of Mathematical Functions Using VRML, Technical Report NISTIR 6289 (February 1999), National Institute of Standards and Technology.

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Roles of Math Search in Mathematics, in Mathematical Knowledge Management, Proceedings of the 5th International Conference on Mathematical Knowledge Management, Lecture Notes in Computer Science, Vol. 4108, Springer-Verlag, 2006.

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NIST’s Digital Library of Mathematial Functions, Physics Today 71, 2, 48 (2018), pp. 48–53.

8: 8 Incomplete Gamma and Related
Functions

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9: 28 Mathieu Functions and Hill’s Equation

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10: 8.26 Tables

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Khamis (1965) tabulates $P(a,x)$ for $a=0.05(.05)10(.1)20(.25)70$, $0.0001\le x\le 250$ to 10D.

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Abramowitz and Stegun (1964, pp. 245–248) tabulates $E_n\left(x\right)$ for $n=2,3,4,10,20$, $x=0(.01)2$ to 7D; also $(x+n){\mathrm{e}}^x{E}_n\left(x\right)$ for $n=2,3,4,10,20$, $x^{-1}=0(.01)0.1(.05)0.5$ to 6S.

… ►

Pagurova (1961) tabulates $E_n\left(x\right)$ for $n=0(1)20$, $x=0(.01)2(.1)10$ to 4-9S; ${\mathrm{e}}^x{E}_n\left(x\right)$ for $n=2(1)10$, $x=10(.1)20$ to 7D; ${\mathrm{e}}^x{E}_p\left(x\right)$ for $p=0(.1)1$, $x=0.01(.01)7(.05)12(.1)20$ to 7S or 7D.

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Zhang and Jin (1996, Table 19.1) tabulates $E_n\left(x\right)$ for $n=1,2,3,5,10,15,20$, $x=0(.1)1,1.5,2,3,5,10,20,30,50,100$ to 7D or 8S.