FMF, Mathematical Library, Lj. (MAKLJ)
-
Simple derivation of the Euler-Boole type summation formula and examples of its useLampret, VitoUsing a simple technique, from the classical Euler-Maclaurin formula is derived the equality ▫$$ \begin{aligned} \sum_{k=1}^n(-1)^{k+1} f(k) =&\sum_{k=1}^{2m-1}(-1)^{k+1} f(k) + ... \frac{1}{2}\Bigl[f(2\lfloor \frac{n+1}{2}\rfloor) - f(2m)\Bigr]\\ &-\sum_{i=1}^{\lfloor p/2\rfloor} \Bigl(4^i-1\Bigr) \frac{B_{2i}}{(2i)!}\Bigl[f^{(2i-1)}(2\lfloor \frac{n+1}{2}\rfloor) - f^{(2i-1)}(2m)\Bigr]\\ &+r_p(m, n), \end{aligned} $$▫ true for integers ▫$m, n, p\ge 1$▫, such that ▫$n\ge 2m+1$▫, and for a function ▫$f\in C^p[2m,n+1]$▫, where the remainder ▫$r_p(m, n)$▫ is estimated as ▫$$ |r_p(m, n)| \le \frac{1+2^{-p}}{3\pi^{p-2}}\int_{2m}^{2\left\lfloor \frac{n+1}{2}\right\rfloor} \left|f^{(p)}(x)\right| \,\mathrm{d}x. $$▫ This formula implies also an infinite alternating summation rule having an integral in the error term only.Source: Mediterranean journal of mathematics. - ISSN 1660-5446 (Vol. 19, iss. 2, Apr. 2022, art. 77 (20 str.))Type of material - article, component part ; adult, seriousPublish date - 2022Language - englishCOBISS.SI-ID - 105758211
Author
Lampret, Vito
Topics
alternating |
approximation |
convergence acceleration |
estimate |
Euler-Boole summation |
Euler-Maclaurin summation
![loading ... loading ...](themes/default/img/ajax-loading.gif)
source: Mediterranean journal of mathematics. - ISSN 1660-5446 (Vol. 19, iss. 2, Apr. 2022, art. 77 (20 str.))
![loading ... loading ...](themes/default/img/ajax-loading.gif)
![loading ... loading ...](themes/default/img/ajax-loading.gif)
![loading ... loading ...](themes/default/img/ajax-loading.gif)
Shelf entry
Permalink
- URL:
Impact factor
Access to the JCR database is permitted only to users from Slovenia. Your current IP address is not on the list of IP addresses with access permission, and authentication with the relevant AAI accout is required.
Year | Impact factor | Edition | Category | Classification | ||||
---|---|---|---|---|---|---|---|---|
JCR | SNIP | JCR | SNIP | JCR | SNIP | JCR | SNIP |
Select the library membership card:
If the library membership card is not in the list,
add a new one.
DRS, in which the journal is indexed
Database name | Field | Year |
---|
Links to authors' personal bibliographies | Links to information on researchers in the SICRIS system |
---|---|
Lampret, Vito | 02113 |
Source: Personal bibliographies
and: SICRIS
Select pickup location:
Material pickup by post
Delivery address:
Address is missing from the member's data.
The address retrieval service is currently unavailable, please try again.
By clicking the "OK" button, you will confirm the pickup location selected above and complete the reservation process.
By clicking the "OK" button, you will confirm the above pickup location and delivery address, and complete the reservation process.
By clicking the "OK" button, you will confirm the address selected above and complete the reservation process.
Notification
Automatic login and reservation service currently not available. You can reserve the material on the Biblos portal or try again here later.
Subject headings in COBISS General List of Subject Headings
Select pickup location
The material from the parent unit is free. If the material is delivered to the pickup location from another unit, the library may charge you for this service.
Pickup location | Material status | Reservation |
---|
Reservation in progress
Please wait a moment.
Reservation was successful.
Reservation failed.
Reservation...
Membership card:
Pickup location: