JP Journal of Algebra, Number Theory and Applications
Volume 3, Issue 3, Pages 447 - 459
(December 2003)
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RECURRENCE
RELATIONS OF THE LEAPING CONVERGENTS
Takao Komatsu (Japan)
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Abstract: Let Pn/qn
= [a0; a1, a2,
…, an]
be the n-th convergent of the
continued fraction expansion of a real number a
= [a0; a1, a2,
…]. It is well-known that the recurrence relationsPn
= anpn – 1
+ pn – 2 and
qn
= anqn-1
+ qn – 2 always hold. If
a
= e1/s(s ³
1), then every third convergent also satisfies the
similar recurrence relations. We generalize this
idea. |
Keywords and phrases: continued
fractions, convergent, recurrence relations. |
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