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coding theory


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1: 26.19 Mathematical Applications
Partitions and plane partitions have applications to representation theory (Bressoud (1999), Macdonald (1995), and Sagan (2001)) and to special functions (Andrews et al. (1999) and Gasper and Rahman (2004)). Other areas of combinatorial analysis include graph theory, coding theory, and combinatorial designs. …
2: 18.38 Mathematical Applications
Coding Theory
For applications of Krawtchouk polynomials K n ( x ; p , N ) and q -Racah polynomials R n ( x ; α , β , γ , δ | q ) to coding theory see Bannai (1990, pp. 38–43), Leonard (1982), and Chihara (1987). …
3: Bibliography C
  • L. Chihara (1987) On the zeros of the Askey-Wilson polynomials, with applications to coding theory. SIAM J. Math. Anal. 18 (1), pp. 191–207.
  • 4: Bibliography B
  • E. Bannai (1990) Orthogonal Polynomials in Coding Theory and Algebraic Combinatorics. In Orthogonal Polynomials (Columbus, OH, 1989), NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., Vol. 294, pp. 25–53.
  • 5: 27.16 Cryptography
    Applications to cryptography rely on the disparity in computer time required to find large primes and to factor large integers. … For this reason, these are often called public key codes. Messages are coded by a method (described below) that requires only the knowledge of n . …For this reason, the codes are considered unbreakable, at least with the current state of knowledge on factoring large numbers. … To code a piece x , raise x to the power r and reduce x r modulo n to obtain an integer y (the coded form of x ) between 1 and n . …
    6: Bibliography S
  • K. Schulten and R. G. Gordon (1976) Recursive evaluation of 3 j - and 6 j - coefficients. Comput. Phys. Comm. 11 (2), pp. 269–278.
  • M. J. Seaton (1982) Coulomb functions analytic in the energy. Comput. Phys. Comm. 25 (1), pp. 87–95.
  • M. J. Seaton (2002b) FGH, a code for the calculation of Coulomb radial wave functions from series expansions. Comput. Phys. Comm. 146 (2), pp. 250–253.
  • M. J. Seaton (2002c) NUMER, a code for Numerov integrations of Coulomb functions. Comput. Phys. Comm. 146 (2), pp. 254–260.
  • J. Segura, P. Fernández de Córdoba, and Yu. L. Ratis (1997) A code to evaluate modified Bessel functions based on the continued fraction method. Comput. Phys. Comm. 105 (2-3), pp. 263–272.
  • 7: Bibliography V
  • A. J. van der Poorten (1980) Some Wonderful Formulas an Introduction to Polylogarithms. In Proceedings of the Queen’s Number Theory Conference, 1979 (Kingston, Ont., 1979), R. Ribenboim (Ed.), Queen’s Papers in Pure and Appl. Math., Vol. 54, Kingston, Ont., pp. 269–286.
  • D. A. Varshalovich, A. N. Moskalev, and V. K. Khersonskiĭ (1988) Quantum Theory of Angular Momentum. World Scientific Publishing Co. Inc., Singapore.
  • N. Ja. Vilenkin (1968) Special Functions and the Theory of Group Representations. American Mathematical Society, Providence, RI.
  • M. N. Vrahatis, O. Ragos, T. Skiniotis, F. A. Zafiropoulos, and T. N. Grapsa (1995) RFSFNS: A portable package for the numerical determination of the number and the calculation of roots of Bessel functions. Comput. Phys. Comm. 92 (2-3), pp. 252–266.
  • M. N. Vrahatis, O. Ragos, T. Skiniotis, F. A. Zafiropoulos, and T. N. Grapsa (1997b) The topological degree theory for the localization and computation of complex zeros of Bessel functions. Numer. Funct. Anal. Optim. 18 (1-2), pp. 227–234.
  • 8: Bibliography N
  • N. Nielsen (1906a) Handbuch der Theorie der Gammafunktion. B. G. Teubner, Leipzig (German).
  • N. Nielsen (1965) Die Gammafunktion. Band I. Handbuch der Theorie der Gammafunktion. Band II. Theorie des Integrallogarithmus und verwandter Transzendenten. Chelsea Publishing Co., New York (German).
  • C. J. Noble and I. J. Thompson (1984) COULN, a program for evaluating negative energy Coulomb functions. Comput. Phys. Comm. 33 (4), pp. 413–419.
  • C. J. Noble (2004) Evaluation of negative energy Coulomb (Whittaker) functions. Comput. Phys. Comm. 159 (1), pp. 55–62.
  • Number Theory Web (website)
  • 9: Bibliography W
  • H. S. Wall (1948) Analytic Theory of Continued Fractions. D. Van Nostrand Company, Inc., New York.
  • W. Wasow (1985) Linear Turning Point Theory. Applied Mathematical Sciences No. 54, Springer-Verlag, New York.
  • R. L. Wiegel (1960) A presentation of cnoidal wave theory for practical application. J. Fluid Mech. 7 (2), pp. 273–286.
  • E. Witten (1987) Elliptic genera and quantum field theory. Comm. Math. Phys. 109 (4), pp. 525–536.
  • M. E. Wojcicki (1961) Algorithm 44: Bessel functions computed recursively. Comm. ACM 4 (4), pp. 177–178.
  • 10: Bibliography
  • Arblib (C) Arb: A C Library for Arbitrary Precision Ball Arithmetic.