Abstract
Algebraic independence of the numbers\(\sum\nolimits_{h \geqslant 0} {\frac{{h^j \zeta ^h }}{{R_{d^h + 1} }}} \), where{R n } n ≥0 is a sequence of integers satisfying a binary linear recurrence relation, is studied by Mahler's method.
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Nishioka, K. Algebraic independence of reciprocal sums of binary recurrences. Monatshefte für Mathematik 123, 135–148 (1997). https://doi.org/10.1007/BF01305968
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DOI: https://doi.org/10.1007/BF01305968