Transcendency Results for Sums of Reciprocals of Linear Recurrences

✍ Scribed by Paul-Georg Becker; Thomas Töpper

• Publisher: John Wiley and Sons
• Year: 2006
• Tongue: English
• Weight: 532 KB
• Volume: 168
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.19941680102

✦ Synopsis

Abstract

Suppose that {R~n~}n≥0 is a linear recursive sequence and d ≥ 2 is an integer. Under suitable conditions on {R~n~} and d we show that
and similarly constructed numbers are transcendental. Special attention is given to the case of binary recurrences.