J Austral Math Soc Ser A 58 pp358--375, 1995.
Legendre Transforms and Apery's Sequences
Asmus L. Schmidt
(Received 27 August 1992)
Abstract
This article stuidies particular sequences satisfying polynomial recurrences, among those Apery's sequence
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an = |
n
å
k=0
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æ
ç
è
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ö
÷
ø
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2
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æ
ç
è
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ö
÷
ø
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2
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which is shown to be the Legendre transform of the sequence
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ck = |
k
å
j=0
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ç
è
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ö
÷
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3
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. |
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This results in the construction of simultaneous approximation of p2 /8 and z(3).
1991 AMS Subject Classification: 11B37, 11J13, 33C45
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Authors
- Asmus L. Schmidt
-
Matematisk Institut, Universitetsparken 5, DK-2100 Copenhagen Ø, Denmark.
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