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1: 24.1 Special Notation
Bernoulli Numbers and Polynomials
The origin of the notation B n , B n ( x ) , 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 E n , E n ( x ) , as defined in §24.2(ii), were used in Lucas (1891) and Nörlund (1924). …
2: Diego Dominici
 1972 in Buenos Aires, Argentina, d.  2023) studied Pure Mathematics at the Universidad de Buenos Aires, Argentina, and did his Ph. …
3: Karl Dilcher
 1954 in Wabern-Harle, Germany) is Professor in the Department of Mathematics and Statistics at Dalhousie University in Halifax, Nova Scotia, Canada. … Dilcher’s research interests include classical analysis, special functions, and elementary, combinatorial, and computational number theory. Over the years he authored or coauthored numerous papers on Bernoulli numbers and related topics, and he maintains a large on-line bibliography on the subject. …
4: Bibliography F
  • H. E. Fettis and J. C. Caslin (1964) Tables of Elliptic Integrals of the First, Second, and Third Kind. Technical report Technical Report ARL 64-232, Aerospace Research Laboratories, Wright-Patterson Air Force Base, Ohio.
  • H. E. Fettis and J. C. Caslin (1969) A Table of the Complete Elliptic Integral of the First Kind for Complex Values of the Modulus. Part I. Technical report Technical Report ARL 69-0172, Aerospace Research Laboratories, Office of Aerospace Research, Wright-Patterson Air Force Base, Ohio.
  • S. Fillebrown (1992) Faster computation of Bernoulli numbers. J. Algorithms 13 (3), pp. 431–445.
  • A. S. Fokas, A. R. Its, and X. Zhou (1992) Continuous and Discrete Painlevé Equations. In Painlevé Transcendents: Their Asymptotics and Physical Applications, D. Levi and P. Winternitz (Eds.), NATO Adv. Sci. Inst. Ser. B Phys., Vol. 278, pp. 33–47.
  • Y. V. Fyodorov (2005) Introduction to the Random Matrix Theory: Gaussian Unitary Ensemble and Beyond. In Recent Perspectives in Random Matrix Theory and Number Theory, London Math. Soc. Lecture Note Ser., Vol. 322, pp. 31–78.
  • 5: Sidebar 9.SB1: Supernumerary Rainbows
    Photograph by Dr. Roy Bishop, Physics Department, Acadia University, Nova Scotia, Canada. See Bishop (1981). ©R. L. Bishop.
    6: 24 Bernoulli and Euler Polynomials
    7: Stephen M. Watt
     1959 in Montreal, Canada) is Professor of Computer Science in the David R. …
    8: Bibliography C
  • L. Carlitz (1953) Some congruences for the Bernoulli numbers. Amer. J. Math. 75 (1), pp. 163–172.
  • L. Carlitz (1954a) q -Bernoulli and Eulerian numbers. Trans. Amer. Math. Soc. 76 (2), pp. 332–350.
  • L. Carlitz (1954b) A note on Euler numbers and polynomials. Nagoya Math. J. 7, pp. 35–43.
  • R. Cazenave (1969) Intégrales et Fonctions Elliptiques en Vue des Applications. Préface de Henri Villat. Publications Scientifiques et Techniques du Ministère de l’Air, No. 452, Centre de Documentation de l’Armement, Paris.
  • Combinatorial Object Server (website) Department of Computer Science, University of Victoria, Canada.
  • 9: Roderick S. C. Wong
    Wong was elected a Fellow of the Royal Society of Canada in 1993, a Foreign Member of the Academy of Science of Turin, Italy, in 2001, a Chevalier dans l’Ordre National de la Légion d’Honneur in 2004, and a Member of the European Academy of Sciences in 2007. He was recipient of the Killam Research Fellowship from the Canada Council in 1982–1984, and of the Rh Award for Outstanding Contributions to Scholarship and Research from the University of Manitoba in 1984. …
    10: Bibliography S
  • M. R. Schroeder (2006) Number Theory in Science and Communication: With Applications in Cryptography, Physics, Digital Information, Computing, and Self-Similarity. 4th edition, Springer-Verlag, Berlin.
  • M. E. Sherry (1959) The zeros and maxima of the Airy function and its first derivative to 25 significant figures. Report AFCRC-TR-59-135, ASTIA Document No. AD214568 Air Research and Development Command, U.S. Air Force, Bedford, MA.
  • I. Sh. Slavutskiĭ (1995) Staudt and arithmetical properties of Bernoulli numbers. Historia Sci. (2) 5 (1), pp. 69–74.
  • I. Sh. Slavutskiĭ (1999) About von Staudt congruences for Bernoulli numbers. Comment. Math. Univ. St. Paul. 48 (2), pp. 137–144.
  • I. Sh. Slavutskiĭ (2000) On the generalized Bernoulli numbers that belong to unequal characters. Rev. Mat. Iberoamericana 16 (3), pp. 459–475.