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1: 18.42 Software

… ►For another listing of Web-accessible software for the functions in this chapter, see GAMS (class C3). …

2: Bibliography B

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Pionic atoms. Annual Review of Nuclear and Particle Science 20, pp. 467–508.

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§33.22(iv).

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Abelian Functions: Abel’s Theorem and the Allied Theory of Theta Functions. Cambridge University Press, Cambridge.

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Notes:

Reprint of the 1897 original, with a foreword by Igor Krichever.

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ISBN 0-521-49877-5, MathReview (John B. Little), ZentralBlatt

Referenced by:

§20.9(ii).

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Coulomb functions (negative energies). Comput. Phys. Comm. 20 (3), pp. 447–458.

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Notes:

Double-precision Fortran code.

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Document, Code

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1st item, 4th item.

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Waves and Thom’s theorem. Advances in Physics 25 (1), pp. 1–26.

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Referenced by:

§36.14(i).

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Singularities in Waves and Rays. In Les Houches Lecture Series Session XXXV, R. Balian, M. Kléman, and J.-P. Poirier (Eds.), Vol. 35, pp. 453–543.

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Referenced by:

§36.14(i).

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3: 27.15 Chinese Remainder Theorem

§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. …

4: 28.27 Addition Theorems

§28.27 Addition Theorems

►Addition theorems provide important connections between Mathieu functions with different parameters and in different coordinate systems. They are analogous to the addition theorems for Bessel functions (§10.23(ii)) and modified Bessel functions (§10.44(ii)). …

5: Peter L. Walker

… ►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. … ►

20 Theta Functions

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6: 27.2 Functions

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§27.2(i) Definitions

… ►Euclid’s Elements (Euclid (1908, Book IX, Proposition 20)) gives an elegant proof that there are infinitely many primes. … ►(See Gauss (1863, Band II, pp. 437–477) and Legendre (1808, p. 394).) ►This result, first proved in Hadamard (1896) and de la Vallée Poussin (1896a, b), is known as the prime number theorem. … ►If $\left(a,n\right)=1$, then the Euler–Fermat theorem states that …

7: 20 Theta Functions

Chapter 20 Theta Functions

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8: Tom M. Apostol

… ►Apostol was born on August 20, 1923. … ►In 1998, the Mathematical Association of America (MAA) awarded him the annual Trevor Evans Award, presented to authors of an exceptional article that is accessible to undergraduates, for his piece entitled “What Is the Most Surprising Result in Mathematics?” (Answer: the prime number theorem). …

9: 1.12 Continued Fractions

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Pringsheim’s Theorem

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Van Vleck’s Theorem

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10: 30.10 Series and Integrals

… ►For an addition theorem, see Meixner and Schäfke (1954, p. 300) and King and Van Buren (1973). …