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1: Bibliography M
  • A. J. MacLeod (1996b) Rational approximations, software and test methods for sine and cosine integrals. Numer. Algorithms 12 (3-4), pp. 259–272.
  • Fr. Mechel (1966) Calculation of the modified Bessel functions of the second kind with complex argument. Math. Comp. 20 (95), pp. 407–412.
  • S. C. Milne (2002) Infinite families of exact sums of squares formulas, Jacobi elliptic functions, continued fractions, and Schur functions. Ramanujan J. 6 (1), pp. 7–149.
  • S. C. Milne (1996) New infinite families of exact sums of squares formulas, Jacobi elliptic functions, and Ramanujan’s tau function. Proc. Nat. Acad. Sci. U.S.A. 93 (26), pp. 15004–15008.
  • D. S. Moak (1981) The q -analogue of the Laguerre polynomials. J. Math. Anal. Appl. 81 (1), pp. 20–47.
  • 2: 20.11 Generalizations and Analogs
    §20.11(i) Gauss Sum
    §20.11(ii) Ramanujan’s Theta Function and q -Series
    Ramanujan’s theta function f ( a , b ) is defined by …
    §20.11(iii) Ramanujan’s Change of Base
    These results are called Ramanujan’s changes of base. …
    3: Bibliography K
  • M. Katsurada (2003) Asymptotic expansions of certain q -series and a formula of Ramanujan for specific values of the Riemann zeta function. Acta Arith. 107 (3), pp. 269–298.
  • R. B. Kearfott, M. Dawande, K. Du, and C. Hu (1994) Algorithm 737: INTLIB: A portable Fortran 77 interval standard-function library. ACM Trans. Math. Software 20 (4), pp. 447–459.
  • M. K. Kerimov (1980) Methods of computing the Riemann zeta-function and some generalizations of it. USSR Comput. Math. and Math. Phys. 20 (6), pp. 212–230.
  • T. H. Koornwinder (2009) The Askey scheme as a four-manifold with corners. Ramanujan J. 20 (3), pp. 409–439.
  • C. Krattenthaler (1993) HYP and HYPQ. Mathematica packages for the manipulation of binomial sums and hypergeometric series respectively q -binomial sums and basic hypergeometric series. Séminaire Lotharingien de Combinatoire 30, pp. 61–76.
  • 4: Bibliography R
  • S. Ramanujan (1921) Congruence properties of partitions. Math. Z. 9 (1-2), pp. 147–153.
  • S. Ramanujan (1927) Some properties of Bernoulli’s numbers (J. Indian Math. Soc. 3 (1911), 219–234.). In Collected Papers,
  • S. Ramanujan (1962) Collected Papers of Srinivasa Ramanujan. Chelsea Publishing Co., New York.
  • J. Raynal (1979) On the definition and properties of generalized 6 - j  symbols. J. Math. Phys. 20 (12), pp. 2398–2415.
  • R. Reynolds and A. Stauffer (2021) Infinite Sum of the Incomplete Gamma Function Expressed in Terms of the Hurwitz Zeta Function. Mathematics 9 (16).
  • 5: Bibliography C
  • H. H. Chan (1998) On Ramanujan’s cubic transformation formula for F 1 2 ( 1 3 , 2 3 ; 1 ; z ) . Math. Proc. Cambridge Philos. Soc. 124 (2), pp. 193–204.
  • R. Chelluri, L. B. Richmond, and N. M. Temme (2000) Asymptotic estimates for generalized Stirling numbers. Analysis (Munich) 20 (1), pp. 1–13.
  • D. V. Chudnovsky and G. V. Chudnovsky (1988) Approximations and Complex Multiplication According to Ramanujan. In Ramanujan Revisited (Urbana-Champaign, Ill., 1987), G. E. Andrews, R. A. Askey, B. C. Bernd, K. G. Ramanathan, and R. A. Rankin (Eds.), pp. 375–472.
  • M. Colman, A. Cuyt, and J. Van Deun (2011) Validated computation of certain hypergeometric functions. ACM Trans. Math. Software 38 (2), pp. Art. 11, 20.
  • M. D. Cooper, R. H. Jeppesen, and M. B. Johnson (1979) Coulomb effects in the Klein-Gordon equation for pions. Phys. Rev. C 20 (2), pp. 696–704.
  • 6: Bibliography B
  • A. Basu and T. M. Apostol (2000) A new method for investigating Euler sums. Ramanujan J. 4 (4), pp. 397–419.
  • R. J. Baxter (1981) Rogers-Ramanujan identities in the hard hexagon model. J. Statist. Phys. 26 (3), pp. 427–452.
  • A. Berkovich and B. M. McCoy (1998) Rogers-Ramanujan Identities: A Century of Progress from Mathematics to Physics. In Proceedings of the International Congress of Mathematicians, Vol. III (Berlin, 1998), pp. 163–172.
  • B. C. Berndt (1989) Ramanujan’s Notebooks. Part II. Springer-Verlag, New York.
  • B. C. Berndt (1991) Ramanujan’s Notebooks. Part III. Springer-Verlag, Berlin-New York.
  • 7: Bibliography D
  • C. de la Vallée Poussin (1896b) Recherches analytiques sur la théorie des nombres premiers. Deuxième partie. Les fonctions de Dirichlet et les nombres premiers de la forme linéaire M x + N . Ann. Soc. Sci. Bruxelles 20, pp. 281–397 (French).
  • K. Dilcher (1996) Sums of products of Bernoulli numbers. J. Number Theory 60 (1), pp. 23–41.
  • H. Ding, K. I. Gross, and D. St. P. Richards (1996) Ramanujan’s master theorem for symmetric cones. Pacific J. Math. 175 (2), pp. 447–490.
  • B. Döring (1966) Complex zeros of cylinder functions. Math. Comp. 20 (94), pp. 215–222.
  • T. M. Dunster (1989) Uniform asymptotic expansions for Whittaker’s confluent hypergeometric functions. SIAM J. Math. Anal. 20 (3), pp. 744–760.
  • 8: Bibliography L
  • P. W. Lawrence, R. M. Corless, and D. J. Jeffrey (2012) Algorithm 917: complex double-precision evaluation of the Wright ω function. ACM Trans. Math. Software 38 (3), pp. Art. 20, 17.
  • D. J. Leeming (1977) An asymptotic estimate for the Bernoulli and Euler numbers. Canad. Math. Bull. 20 (1), pp. 109–111.
  • D. H. Lehmer (1943) Ramanujan’s function τ ( n ) . Duke Math. J. 10 (3), pp. 483–492.
  • D. H. Lehmer (1947) The vanishing of Ramanujan’s function τ ( n ) . Duke Math. J. 14 (2), pp. 429–433.
  • J. Lepowsky and R. L. Wilson (1982) A Lie theoretic interpretation and proof of the Rogers-Ramanujan identities. Adv. in Math. 45 (1), pp. 21–72.