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1: 24.1 Special Notation
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Bernoulli Numbers and Polynomials
►The origin of the notation , , is not clear. … ►Euler Numbers and Polynomials
… ►Its coefficients were first studied in Euler (1755); they were called Euler numbers by Raabe in 1851. The notations , , as defined in §24.2(ii), were used in Lucas (1891) and Nörlund (1924). …2: Bibliography J
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Fonctions de Mathieu et polynômes de Klein-Gordon.
C. R. Acad. Sci. Paris Sér. I Math. 325 (7), pp. 713–716 (French).
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Stirling Numbers, Lambert W and the Gamma Function.
In Mathematical Aspects of Computer and Information Sciences, J. Blömer, I. S. Kotsireas, T. Kutsia, and D. E. Simos (Eds.),
Cham, pp. 275–279.
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3: Bibliography D
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Multiplicative Number Theory.
3rd edition, Graduate Texts in Mathematics, Vol. 74, Springer-Verlag, New York.
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Quantum Fields and Strings: A Course for Mathematicians. Vol. 1, 2.
American Mathematical Society, Providence, RI.
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Elements of the Theory of Numbers.
Harcourt/Academic Press, San Diego, CA.
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Sums of products of Bernoulli numbers.
J. Number Theory 60 (1), pp. 23–41.
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Bernoulli Numbers and Confluent Hypergeometric Functions.
In Number Theory for the Millennium, I (Urbana, IL, 2000),
pp. 343–363.
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4: Bibliography Q
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“Best possible” upper and lower bounds for the zeros of the Bessel function
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Trans. Amer. Math. Soc. 351 (7), pp. 2833–2859.
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5: Bibliography W
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Asymptotische Entwicklungen der Gaußschen hypergeometrischen Funktion für unbeschränkte Parameter.
Z. Anal. Anwendungen 9 (4), pp. 351–360 (German).
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Prime Divisors of the Bernoulli and Euler Numbers.
In Number Theory for the Millennium, III (Urbana, IL, 2000),
pp. 357–374.
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Generating functions of class-numbers.
Compositio Math. 1, pp. 39–68.
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Quadrature formulas for oscillatory integral transforms.
Numer. Math. 39 (3), pp. 351–360.
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6: Bibliography T
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Coulomb functions with complex angular momenta.
Comput. Phys. Comm. 17 (4), pp. 351–355.
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New congruences for the Bernoulli numbers.
Math. Comp. 48 (177), pp. 341–350.
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Asymptotic estimates of Stirling numbers.
Stud. Appl. Math. 89 (3), pp. 233–243.
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Explicit formulas for the Bernoulli and Euler polynomials and numbers.
Abh. Math. Sem. Univ. Hamburg 61, pp. 175–180.
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On the theory of the Bernoulli polynomials and numbers.
J. Math. Anal. Appl. 104 (2), pp. 309–350.
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7: Bibliography C
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Some congruences for the Bernoulli numbers.
Amer. J. Math. 75 (1), pp. 163–172.
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-Bernoulli and Eulerian numbers.
Trans. Amer. Math. Soc. 76 (2), pp. 332–350.
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A note on Euler numbers and polynomials.
Nagoya Math. J. 7, pp. 35–43.
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New proof of the addition theorem for Gegenbauer polynomials.
SIAM J. Math. Anal. 2, pp. 347–351.
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Über die Fälle, wenn die Reihe von der Form etc. ein Quadrat von der Form etc. hat.
J. Reine Angew. Math. 3, pp. 89–91.
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8: 1.9 Calculus of a Complex Variable
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§1.9(i) Complex Numbers
… ►Powers
… ►That is, given any positive number , however small, we can find a positive number such that for all in the open disk . … ►A neighborhood of a point is a disk . … ►Winding Number
…9: Bibliography
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Congruences of -adic integer order Bernoulli numbers.
J. Number Theory 59 (2), pp. 374–388.
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Nonlinear chains and Painlevé equations.
Phys. D 73 (4), pp. 335–351.
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Sharp bounds for the Bernoulli numbers.
Arch. Math. (Basel) 74 (3), pp. 207–211.
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Number Theory.
In The New Encyclopaedia Britannica,
Vol. 25, pp. 14–37.
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A Centennial History of the Prime Number Theorem.
In Number Theory,
Trends Math., pp. 1–14.
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10: Bibliography M
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Computational Algebra Group, School of Mathematics and Statistics, University of Sydney, Australia.
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Catastrophe optics of spheroidal drops and generalized rainbows.
J. Quantit. Spec. and Rad. Trans. 63, pp. 341–351.
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On the representation of numbers as a sum of squares.
Quarterly Journal of Math. 48, pp. 93–104.
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Asymptotic development of the Stirling numbers of the first kind.
J. London Math. Soc. 33, pp. 133–146.
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Stirling numbers of the second kind.
Duke Math. J. 25 (1), pp. 29–43.
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