A note on extending Euler's connection between continued fractions and power series

✍ Scribed by John Gill

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 240 KB
• Volume: 106
• Category: Article
• ISSN: 0377-0427
• DOI: 10.1016/s0377-0427(99)00071-0

✦ Synopsis

Euler's Connection describes an exact equivalence between certain continued fractions and power series. If the partial numerators and denominators of the continued fractions are perturbed slightly, the continued fractions equal power series plus easily computed error terms. These continued fractions may be integrated by the series with another easily computed error term.