Elementary Proof of Yu. V. Nesterenko Expansion of the Number Zeta(3) in Continued Fraction
Yu. V. Nesterenko has proved that ζ(3)=b0+a1|/|b1+⋯+aν|/|bν+⋯, b0=b1=a2=2, a1=1,b2=4, b4k+1=2k+2, a4k+1=k(k+1), b4k+2=2k+4, and a4k+2=(k+1)(k+2) for k∈ℕ; b4k+3=2k+3, a4k+3=(k+1)2, and b4k+4=2k+2, a4k+4=(k+2)2 for k&am...
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| Format: | Article |
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SpringerOpen
2010-01-01
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| Series: | Advances in Difference Equations |
| Online Access: | http://dx.doi.org/10.1155/2010/143521 |
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doaj-97f9c3e6f073487b85d5c6fc02623a3a2020-11-25T01:27:25ZengSpringerOpenAdvances in Difference Equations1687-18391687-18472010-01-01201010.1155/2010/143521Elementary Proof of Yu. V. Nesterenko Expansion of the Number Zeta(3) in Continued FractionLeonid GutnikYu. V. Nesterenko has proved that ζ(3)=b0+a1|/|b1+⋯+aν|/|bν+⋯, b0=b1=a2=2, a1=1,b2=4, b4k+1=2k+2, a4k+1=k(k+1), b4k+2=2k+4, and a4k+2=(k+1)(k+2) for k∈ℕ; b4k+3=2k+3, a4k+3=(k+1)2, and b4k+4=2k+2, a4k+4=(k+2)2 for k∈ℕ0. His proof is based on some properties of hypergeometric functions. We give here an elementary direct proof of this result. http://dx.doi.org/10.1155/2010/143521 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Leonid Gutnik |
| spellingShingle |
Leonid Gutnik Elementary Proof of Yu. V. Nesterenko Expansion of the Number Zeta(3) in Continued Fraction Advances in Difference Equations |
| author_facet |
Leonid Gutnik |
| author_sort |
Leonid Gutnik |
| title |
Elementary Proof of Yu. V. Nesterenko Expansion of the Number Zeta(3) in Continued Fraction |
| title_short |
Elementary Proof of Yu. V. Nesterenko Expansion of the Number Zeta(3) in Continued Fraction |
| title_full |
Elementary Proof of Yu. V. Nesterenko Expansion of the Number Zeta(3) in Continued Fraction |
| title_fullStr |
Elementary Proof of Yu. V. Nesterenko Expansion of the Number Zeta(3) in Continued Fraction |
| title_full_unstemmed |
Elementary Proof of Yu. V. Nesterenko Expansion of the Number Zeta(3) in Continued Fraction |
| title_sort |
elementary proof of yu. v. nesterenko expansion of the number zeta(3) in continued fraction |
| publisher |
SpringerOpen |
| series |
Advances in Difference Equations |
| issn |
1687-1839 1687-1847 |
| publishDate |
2010-01-01 |
| description |
Yu. V. Nesterenko has proved that ζ(3)=b0+a1|/|b1+⋯+aν|/|bν+⋯, b0=b1=a2=2, a1=1,b2=4, b4k+1=2k+2, a4k+1=k(k+1), b4k+2=2k+4, and a4k+2=(k+1)(k+2) for k∈ℕ; b4k+3=2k+3, a4k+3=(k+1)2, and b4k+4=2k+2, a4k+4=(k+2)2 for k∈ℕ0. His proof is based on some properties of hypergeometric functions. We give here an elementary direct proof of this result. |
| url |
http://dx.doi.org/10.1155/2010/143521 |
| work_keys_str_mv |
AT leonidgutnik elementaryproofofyuvnesterenkoexpansionofthenumberzeta3incontinuedfraction |
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1725105654679470080 |