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Berndt, Bruce C.; Joshi, Padmini T.; Wilson, B. M.

Chapter 2 of Ramanujan’s second notebook. (English) Zbl 0463.40002

Glasg. Math. J. 22, 199-216 (1981).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
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MSC:

40A05 Convergence and divergence of series and sequences
40-03 History of sequences, series, summability
01A05 General histories, source books
65H99 Nonlinear algebraic or transcendental equations

Keywords:

inverse tangent functions; Bernoulli’s method for approximating the roots; transcendental equations
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References:

[1] Ramanujan, Notebooks (2 volumes) (1957)
[2] DOI: 10.1090/S0002-9904-1959-10290-1 · Zbl 0086.06201 · doi:10.1090/S0002-9904-1959-10290-1
[3] Ramanujan, J. Indian Math. Soc. 3 pp 43– (1911)
[4] Ramanujan, J. Indian Math. Soc. 3 pp 43– (1911)
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[11] DOI: 10.1137/0109014 · Zbl 0109.04705 · doi:10.1137/0109014
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[13] DOI: 10.1090/S0002-9904-1960-10469-7 · Zbl 0100.06802 · doi:10.1090/S0002-9904-1960-10469-7
[14] Wright, Proc. Roy. Soc. Edinburgh, Sect. A 65 pp 192– (1959)
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[16] Whittaker, The calculus of observations (1926)
[17] Wheelon, Tables of summable series and integrals involving Bessel functions (1968) · Zbl 0187.12901
[18] Titchmarsh, The theory of functions (1939) · Zbl 0022.14602
[19] Hadamard, La Serie de Taylor (1926)
[20] Glasser, Fibonacci Quart 14 pp 385– (1976)
[21] Glaisher, J. Math. Oxford 15 pp 151– (1878)
[22] Chrystal, Algebra, Part II (1922)
[23] Bromwich, An introduction to the theory of infinite series (1926) · JFM 52.0208.05
[24] Berndt, Enseignement Math. 26 pp 1– (1980)
[25] Berndt, Math. Mag. 51 pp 147– (1978)
[26] Ayoub, An introduction to the analytic theory of numbers (1963) · Zbl 0128.04303
[27] Ramanujan, Collected papers (1962)
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