| Abstrakt: |
Abstract??In recent analyses [3, 4] the remarkable AGM continued fraction of Ramanujan?denoted$${\cal r}_1$$(a,b)?was proven to converge for almost all complex parameter pairs (a,b). It was conjectured that$${\cal r}_1$$diverges if and only if (0?a=bei?with cos2? ? 1) or (a2=b2? (??, 0)). In the present treatment we resolve this conjecture to the positive, thus establishing the precise convergence domain for$${\cal r}_1$$. This is accomplished by analyzing, using various special functions, the dynamics of sequences such as (tn) satisfying a recurrence [ABSTRACT FROM AUTHOR] |
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