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Article

Bracken, Paul
A function related to the central limit theorem. (English). Commentationes Mathematicae Universitatis Carolinae, vol. 39 (1998), issue 4, pp. 765-775
MSC: 11B83, 32A05, 33B10 | MR 1715465 | Zbl 1059.33500
Keywords:
series; Ramanujan
Summary:
A number of properties of a function which originally appeared in a problem proposed by Ramanujan are presented. Several equivalent representations of the function are derived. These can be used to evaluate the function. A new derivation of an expansion in inverse powers of the argument of the function is obtained, as well as rational expressions for higher order coefficients.
References:
[1] Ramanujan S.: Question 294. J. Indian Math. Soc. 3 , 128 (1911).
[2] Ramanujan S.: On Question 294. J. Indian Math. Soc. 4 , 151 (1912).
[3] Berndt B.C.: Ramanujan's Notebooks. Vol II, Springer, 1985. MR 0781125 | Zbl 0944.01005
[4] Bowman K.O., Shenton L.R., Szekeres G.: J. Stat. Comput. Siml. 20 , 167 (1984).
[5] Copson E.T.: An Introduction to the Theory of Functions of a Complex Variable. Clarendon Press, Oxford, 1970. Zbl 0188.37901
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