A class of series acceleration formulae for Catalan's constant

Ramanujan Journal

Volumn 3, Issue 2, 1999, Pages 159-173

  Bradley, David M ^a  

^a UNIVERSITY OF MAINE   (United States)

Author keywords

Algebraic unit; Catalan's constant; Central binomial coefficient; Log tangent integral

Indexed keywords

EID: 0007128860     PISSN: 13824090     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1006945407723     Document Type: Article

References (16)

1. M. Abramowitz and I. Stegun, Handbook of Mathematical Functions, Dover, New York, p. 807, 1972.
2. D.H. Bailey and H.R.P. Ferguson, "Numerical results on relations between numerical constants using a new algorithm," Mathematics of Computation 53 (1989), 649-656.
3. D.H. Bailey and H.R.P. Ferguson, "A polynomial time, numerically stable integer relation algorithm," RNR Technical Report, RNR-91-032.
4. B.C. Berndt, Ramanujan's Notebooks: Part I, Springer-Verlag, p. 289, 1985.
5. A. Borodin, R. Fagin, J.E. Hopcroft, and M. Tompa, "Decreasing the nesting depth of expressions involving square roots," J. Symbolic Comp. 1 (1985), 169-188.
6. J.M. Borwein and P.B. Borwein, Pi and the AGM, Wiley-Interscience, John Wiley & Sons, Toronto, p. 384 1987.
7. J.M. Borwein and D.M. Bradley, "Searching symbolically for Apéry-like formulae for values of the Riemann zeta function," SIGSAM Bulletin of Symbolic and Algebraic Manipulation, 30(2) (1996), 2-7.
8. J.M. Borwein and D.M. Bradley, "Empirically determined Apéry-like formulae for ζ (4n + 3)," Experimental Mathematics 6 (1997), 181-194.
9. H.R.P. Ferguson and R.W. Forcade, "Generalization of the Euclidean algorithm for real numbers to all dimensions higher than two," Bulletin of the American Mathematical Society 1 (1979), 912-914.
10. G.H. Hardy and E.M. Wright, An Introduction to the Theory of Numbers, 5th edition, Oxford University Press, New York, p. 148, 1979.
11. J. Hastad, B. Just, J.C. Lagarias, and C.P. Schnorr, "Polynomial time algorithms for finding integer relations among real numbers," SIAM Journal on Computing 18 (1988), 859-881.
12. A.K. Lenstra, H.W. Lenstra, and L. Lovasz, "Factoring polynomials with rational coefficients," Math. Annalen, 261 (1982), 515-534.
13. L. Lewin, Polylogarithms and Associated Functions, Elsevier, North Holland, New York, 1981.
14. -1/tdt," Journal of the Indian Mathematical Society 7 (1915), 93-96.
15. N.J.A. Sloane and S. Plouffe, The Encyclopedia of Integer Sequences, Academic Press, San Diego, 1995.
16. R. Zippel, "Simplifications of expressions involving radicals," J. Symbolic Comp. 1 (1985), 189-210.