قراءة كتاب The First 1000 Euler Numbers

تنويه: تعرض هنا نبذة من اول ١٠ صفحات فقط من الكتاب الالكتروني، لقراءة الكتاب كاملا اضغط على الزر “اشتر الآن"

‏اللغة: English
The First 1000 Euler Numbers

The First 1000 Euler Numbers

تقييمك:
0
No votes yet
المؤلف:
دار النشر: Project Gutenberg
الصفحة رقم: 2

form of incomplete, inaccurate or corrupt data, transcription errors, a copyright or other intellectual property infringement, a defective or damaged disk or other etext medium, a computer virus, or computer codes that damage or cannot be read by your equipment.

LIMITED WARRANTY; DISCLAIMER OF DAMAGES But for the "Right of Replacement or Refund" described below, [1] the Project (and any other party you may receive this etext from as a PROJECT GUTENBERG-tm etext) disclaims all liability to you for damages, costs and expenses, including legal fees, and [2] YOU HAVE NO REMEDIES FOR NEGLIGENCE OR UNDER STRICT LIABILITY, OR FOR BREACH OF WARRANTY OR CONTRACT, INCLUDING BUT NOT LIMITED TO INDIRECT, CONSEQUENTIAL, PUNITIVE OR INCIDENTAL DAMAGES, EVEN IF YOU GIVE NOTICE OF THE POSSIBILITY OF SUCH DAMAGES.

If you discover a Defect in this etext within 90 days of receiving it, you can receive a refund of the money (if any) you paid for it by sending an explanatory note within that time to the person you received it from. If you received it on a physical medium, you must return it with your note, and such person may choose to alternatively give you a replacement copy. If you received it electronically, such person may choose to alternatively give you a second opportunity to receive it electronically.

THIS ETEXT IS OTHERWISE PROVIDED TO YOU "AS-IS". NO OTHER WARRANTIES OF ANY KIND, EXPRESS OR IMPLIED, ARE MADE TO YOU AS TO THE ETEXT OR ANY MEDIUM IT MAY BE ON, INCLUDING BUT NOT LIMITED TO WARRANTIES OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE.

Some states do not allow disclaimers of implied warranties or the exclusion or limitation of consequential damages, so the above disclaimers and exclusions may not apply to you, and you may have other legal rights.

INDEMNITY You will indemnify and hold the Project, its directors, officers, members and agents harmless from all liability, cost and expense, including legal fees, that arise directly or indirectly from any of the following that you do or cause: [1] distribution of this etext, [2] alteration, modification, or addition to the etext, or [3] any Defect.

DISTRIBUTION UNDER "PROJECT GUTENBERG-tm" You may distribute copies of this etext electronically, or by disk, book or any other medium if you either delete this "Small Print!" and all other references to Project Gutenberg, or:

[1] Only give exact copies of it. Among other things, this requires that you do not remove, alter or modify the etext or this "small print!" statement. You may however, if you wish, distribute this etext in machine readable binary, compressed, mark-up, or proprietary form, including any form resulting from conversion by word pro- cessing or hypertext software, but only so long as *EITHER*:

[*] The etext, when displayed, is clearly readable, and does *not* contain characters other than those intended by the author of the work, although tilde (~), asterisk (*) and underline (_) characters may be used to convey punctuation intended by the author, and additional characters may be used to indicate hypertext links; OR

[*] The etext may be readily converted by the reader at no expense into plain ASCII, EBCDIC or equivalent form by the program that displays the etext (as is the case, for instance, with most word processors); OR

[*] You provide, or agree to also provide on request at no additional cost, fee or expense, a copy of the etext in its original plain ASCII form (or in EBCDIC or other equivalent proprietary form).

[2] Honor the etext refund and replacement provisions of this "Small Print!" statement.

[3] Pay a trademark license fee to the Project of 20% of the net profits you derive calculated using the method you already use to calculate your applicable taxes. If you don't derive profits, no royalty is due. Royalties are payable to "Project Gutenberg Association/Carnegie-Mellon University" within the 60 days following each date you prepare (or were legally required to prepare) your annual (or equivalent periodic) tax return.

WHAT IF YOU *WANT* TO SEND MONEY EVEN IF YOU DON'T HAVE TO? The Project gratefully accepts contributions in money, time, scanning machines, OCR software, public domain etexts, royalty free copyright licenses, and every other sort of contribution you can think of. Money should be paid to "Project Gutenberg Association / Carnegie-Mellon University".

We are planning on making some changes in our donation structure in 2000, so you might want to email me, [email protected] beforehand.

*END THE SMALL PRINT! FOR PUBLIC DOMAIN ETEXTS*Ver.04.29.93*END*

Mathematical constants and numbers edited by Simon Plouffe Associate Professor LaCIM, University of Quebec at Montreal http://www.lacim.uqam.ca/pi : Plouffe's Inverter [email protected]

The first 1000 Euler numbers as defined by

2/(exp(t)+exp(-t)) = sum(exp(n)/n!*t^n, n = 0..infinity)

are the coefficients of the series expansion.

Euler(0) 1

Euler(2) -1

Euler(4) 5

Euler(6) -61

Euler(8) 1385

Euler(10) -50521

Euler(12) 2702765

Euler(14) -199360981

Euler(16) 19391512145

Euler(18) -2404879675441

Euler(20) 370371188237525

Euler(22) -69348874393137901

Euler(24) 15514534163557086905

Euler(26) -4087072509293123892361

Euler(28) 1252259641403629865468285

Euler(30) -441543893249023104553682821

Euler(32) 177519391579539289436664789665

Euler(34) -80723299235887898062168247453281

Euler(36) 41222060339517702122347079671259045

Euler(38) -23489580527043108252017828576198947741

Euler(40) 14851150718114980017877156781405826684425

Euler(42) -10364622733519612119397957304745185976310201

Euler(44) 7947579422597592703608040510088070619519273805

Euler(46) -6667537516685544977435028474773748197524107684661

Euler(48) 6096278645568542158691685742876843153976539044435185

Euler(50) -6053285248188621896314383785111649088103498225146815121

Euler(52) 6506162486684608847715870634080822983483644236765385576565

Euler(54) -7546659939008739098061432565889736744212240024711699858645581

Euler(56) 9420321896420241204202286237690583227209388852599646009394905945

Euler(58) -12622019251806218719903409237287489255482341061191825594069964920041

Euler(60) 18108911496579230496545807741652158688733487349236314106008095454231325

Euler(62) -27757101702071580597366980908371527449233019594800917578033782766889782501

Euler(64) 45358103330017889174746887871567762366351861519470368881468843837919695760705

Euler(66) -788628420666178941810072074223999042394781629720037689327097574948571679453769 61

Euler(68)

Pages