On the asymptotics of the rows of the Padé table of analytic functions with logarithmic branch points
For the functions , where l n and a n are arithmetic progressions and their Padé approximants π n,m ( z; f ), we establish an asymptotics of the decrease of the difference f ( z ) − π n,m ( z; f ) for the case in which z ∈ D = { z : | z | < 1}, m is fixed, and n → ∞. In particular, we obtain prox...
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| Veröffentlicht in: | Mathematical Notes 2008-10, Vol.84 (3-4), p.379-388 |
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| container_title | Mathematical Notes |
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| creator | Starovoitov, A. P. Starovoitova, N. A. |
| description | For the functions
, where
l
n
and
a
n
are arithmetic progressions and their Padé approximants
π
n,m
(
z; f
), we establish an asymptotics of the decrease of the difference
f
(
z
) −
π
n,m
(
z; f
) for the case in which
z
∈
D
= {
z
: |
z
| < 1},
m
is fixed, and
n
→ ∞. In particular, we obtain proximate orders of decrease of best uniform rational approximations to the functions ln(1 −
z
) and arctan
z
in the disk
D
q
= {
z
: |
z
| ≤
q
< 1}. |
| doi_str_mv | 10.1134/S0001434608090083 |
| format | Article |
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, where
l
n
and
a
n
are arithmetic progressions and their Padé approximants
π
n,m
(
z; f
), we establish an asymptotics of the decrease of the difference
f
(
z
) −
π
n,m
(
z; f
) for the case in which
z
∈
D
= {
z
: |
z
| < 1},
m
is fixed, and
n
→ ∞. In particular, we obtain proximate orders of decrease of best uniform rational approximations to the functions ln(1 −
z
) and arctan
z
in the disk
D
q
= {
z
: |
z
| ≤
q
< 1}.</description><identifier>ISSN: 0001-4346</identifier><identifier>EISSN: 1573-8876</identifier><identifier>DOI: 10.1134/S0001434608090083</identifier><language>eng</language><publisher>Dordrecht: SP MAIK Nauka/Interperiodica</publisher><subject>Mathematics ; Mathematics and Statistics</subject><ispartof>Mathematical Notes, 2008-10, Vol.84 (3-4), p.379-388</ispartof><rights>Pleiades Publishing, Ltd. 2008</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c240t-89471194f989e803b5c7b6568c48c186589c7ff656daa45863848b681de2dd9e3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1134/S0001434608090083$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1134/S0001434608090083$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Starovoitov, A. P.</creatorcontrib><creatorcontrib>Starovoitova, N. A.</creatorcontrib><title>On the asymptotics of the rows of the Padé table of analytic functions with logarithmic branch points</title><title>Mathematical Notes</title><addtitle>Math Notes</addtitle><description>For the functions
, where
l
n
and
a
n
are arithmetic progressions and their Padé approximants
π
n,m
(
z; f
), we establish an asymptotics of the decrease of the difference
f
(
z
) −
π
n,m
(
z; f
) for the case in which
z
∈
D
= {
z
: |
z
| < 1},
m
is fixed, and
n
→ ∞. In particular, we obtain proximate orders of decrease of best uniform rational approximations to the functions ln(1 −
z
) and arctan
z
in the disk
D
q
= {
z
: |
z
| ≤
q
< 1}.</description><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><issn>0001-4346</issn><issn>1573-8876</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2008</creationdate><recordtype>article</recordtype><recordid>eNp9UMtKAzEUDaJgrX6Au_zAaNJkMjdLKb6gUEFdD5lM0k6ZJiVJKfNJfoc_ZsaKG8HVPfc8LtyD0DUlN5QyfvtKCKGccUGASEKAnaAJLStWAFTiFE1GuRj1c3QR4yZvVFAyQXbpcFobrOKw3SWfOh2xt99U8Idf_KLazw-cVNObkVJO9UP2Yrt3OnXeRXzo0hr3fqVCBtssNUE5vcY737kUL9GZVX00Vz9zit4f7t_mT8Vi-fg8v1sUesZJKkDyilLJrQRpgLCm1FUjSgGag6YgSpC6sjYzrVK8BMGAQyOAtmbWttKwKaLHuzr4GIOx9S50WxWGmpJ6LKr-U1TOzI6ZmL1uZUK98fuQP4z_hL4AJVZrNg</recordid><startdate>20081001</startdate><enddate>20081001</enddate><creator>Starovoitov, A. P.</creator><creator>Starovoitova, N. A.</creator><general>SP MAIK Nauka/Interperiodica</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20081001</creationdate><title>On the asymptotics of the rows of the Padé table of analytic functions with logarithmic branch points</title><author>Starovoitov, A. P. ; Starovoitova, N. A.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c240t-89471194f989e803b5c7b6568c48c186589c7ff656daa45863848b681de2dd9e3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2008</creationdate><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Starovoitov, A. P.</creatorcontrib><creatorcontrib>Starovoitova, N. A.</creatorcontrib><collection>CrossRef</collection><jtitle>Mathematical Notes</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Starovoitov, A. P.</au><au>Starovoitova, N. A.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On the asymptotics of the rows of the Padé table of analytic functions with logarithmic branch points</atitle><jtitle>Mathematical Notes</jtitle><stitle>Math Notes</stitle><date>2008-10-01</date><risdate>2008</risdate><volume>84</volume><issue>3-4</issue><spage>379</spage><epage>388</epage><pages>379-388</pages><issn>0001-4346</issn><eissn>1573-8876</eissn><abstract>For the functions
, where
l
n
and
a
n
are arithmetic progressions and their Padé approximants
π
n,m
(
z; f
), we establish an asymptotics of the decrease of the difference
f
(
z
) −
π
n,m
(
z; f
) for the case in which
z
∈
D
= {
z
: |
z
| < 1},
m
is fixed, and
n
→ ∞. In particular, we obtain proximate orders of decrease of best uniform rational approximations to the functions ln(1 −
z
) and arctan
z
in the disk
D
q
= {
z
: |
z
| ≤
q
< 1}.</abstract><cop>Dordrecht</cop><pub>SP MAIK Nauka/Interperiodica</pub><doi>10.1134/S0001434608090083</doi><tpages>10</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0001-4346 |
| ispartof | Mathematical Notes, 2008-10, Vol.84 (3-4), p.379-388 |
| issn | 0001-4346 1573-8876 |
| language | eng |
| recordid | cdi_crossref_primary_10_1134_S0001434608090083 |
| source | SpringerLink Journals |
| subjects | Mathematics Mathematics and Statistics |
| title | On the asymptotics of the rows of the Padé table of analytic functions with logarithmic branch points |
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