Digit Sums and Infinite Products
Consider the sequence un defined as follows: un=+1 if the sum of the base b digits of n is even, and un=−1 otherwise, where we take b=2. Recall that the Woods-Robbins infinite product involves a rational function in n and the sequence un. Although several generalizations of the Woods-Robbins product...
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| Formato: | Capítulo de libro |
| Lenguaje: | inglés |
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IntechOpen
2020
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| Acceso en línea: | https://www.intechopen.com/chapters/72695 |
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| Sumario: | Consider the sequence un defined as follows: un=+1 if the sum of the base b digits of n is even, and un=−1 otherwise, where we take b=2. Recall that the Woods-Robbins infinite product involves a rational function in n and the sequence un. Although several generalizations of the Woods-Robbins product are known in the literature, no other infinite product involving a rational function in n and the sequence un was known in closed form until recently. In this chapter we introduce a systematic approach to these products, which may be generalized to other values of b. We illustrate the approach by evaluating a large class of similar infinite products. |
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| ISBN: | 978-1-83968-050-2 |
| DOI: | 10.5772/intechopen.92365 |