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1: 19.8 Quadratic Transformations

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§19.8(i) Gauss’s Arithmetic-Geometric Mean (AGM)

… ►As $n\to \mathrm{\infty }$, $a_n$ and $g_n$ converge to a common limit $M(a_0,g_0)$ called the AGM (Arithmetic-Geometric Mean) of $a_0$ and $g_0$. …showing that the convergence of $c_n$ to 0 and of $a_n$ and $g_n$ to $M(a_0,g_0)$ is quadratic in each case. … ►The AGM appears in …and in …

2: 20 Theta Functions

Chapter 20 Theta Functions

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3: 27.15 Chinese Remainder Theorem

… ►This theorem is employed to increase efficiency in calculating with large numbers by making use of smaller numbers in most of the calculation. …Their product $m$ has 20 digits, twice the number of digits in the data. By the Chinese remainder theorem each integer in the data can be uniquely represented by its residues (mod $m_1$), (mod $m_2$), (mod $m_3$), and (mod $m_4$), respectively. …These numbers, in turn, are combined by the Chinese remainder theorem to obtain the final result $(modm)$, which is correct to 20 digits. … ►Details of a machine program describing the method together with typical numerical results can be found in Newman (1967). …

4: Gergő Nemes

… ► 1988 in Szeged, Hungary) is a Research Fellow at the Alfréd Rényi Institute of Mathematics in Budapest, Hungary. … ► in mathematics (with distinction) and a M. …in mathematics (with honours) from Loránd Eötvös University, Budapest, Hungary and a Ph. … in mathematics from Central European University 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. …

5: 8 Incomplete Gamma and Related
Functions

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6: 28 Mathieu Functions and Hill’s Equation

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7: Wolter Groenevelt

… ► 1976 in Leidschendam, the Netherlands) is an Associate Professor at the Delft University of Technology in Delft, The Netherlands. … ► in mathematics at the Delft University of Technology in 2004. ►Groenevelt’s research interests is in special functions and orthogonal polynomials and their relations with representation theory and interacting particle systems. ►As of September 20, 2022, Groenevelt performed a complete analysis and acted as main consultant for the update of the source citation and proof metadata for every formula in Chapter 18 Orthogonal Polynomials. ►In July 2023, Groenevelt was named Contributing Developer of the NIST Digital Library of Mathematical Functions.

8: 23 Weierstrass Elliptic and Modular
Functions

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9: Peter L. Walker

… ► 1942 in Dorchester, U. …He began his academic career in 1964 at the University of Lancaster, U. … ►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. … ►Walker is now retired and living in Cheltenham, UK. … ►

20 Theta Functions

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10: 36 Integrals with Coalescing Saddles

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