Ben Taylor (first baseman, born 1888) and Abel polynomials: Difference between pages

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The Abel polynomials in mathematics form a polynomial sequence, the nth term of which is of the form

p_{n}(x)=x(x-an)^{n-1}.\,

The sequence is named after Niels Henrik Abel (1802-1829), the Norwegian mathematician.

This polynomial sequence is of binomial type: conversely, every polynomial sequence of binomial type may be obtained from the Abel sequence in the umbral calculus.

References

Gian-Carlo Rota (1997). "All polynomials of binomial type are represented by Abel polynomials". Annali della Scuola Normale Superiore di Pisa - Classe di Scienze Sér. 4. 25 (3–4): 731–738. Retrieved 2008-07-26. {{cite journal}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)

External links

Weisstein, Eric W. "Abel Polynomial". MathWorld.

This algebra-related article is a stub. You can help Wikipedia by expanding it.

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+The '''Abel polynomials''' in [[mathematics]] form a [[polynomial sequence]], the ''n''th term of which is of the form
-'''Benjamin Harrison Taylor''' (July 1, 1888 - January 24, 1953) was an American [[first baseman]] and [[manager (baseball)|manager]] in [[baseball]]'s [[Negro league baseball|Negro Leagues]]. He was elected to the [[Baseball Hall of Fame]] in [[Baseball Hall of Fame balloting, 2006|2006]].
+:<math>p_n(x)=x(x-an)^{n-1}. \,</math>
-Born in [[Anderson, South Carolina]], he played for the [[Chicago American Giants]], [[Indianapolis ABC's]], [[St. Louis Giants]], [[Bacharach Giants]], [[Washington Potomacs]], [[Harrisburg Giants]], [[Baltimore Black Sox]], [[Baltimore Stars]], [[Brooklyn Eagles]], [[Washington Black Senators]] and [[New York Cubans]]. His playing career played lasted from {{by|1913}} to {{by|1929}}.
+The sequence is named after [[Niels Henrik Abel]] (1802-1829), the Norwegian mathematician.
-In all but one of his first 16 seasons, Taylor batted over .300. In a 1949 [[Philadelphia Evening Bulletin]] article, Oscar Charleston selected Ben Taylor as his first baseman on his all-time All-Star team, but Taylor initiated his career as a pitcher for the Birmingham Giants in 1908. After playing for the St. Louis Giants (1911-12), New York Lincoln Giants (1912) and Rube Foster's Chicago American Giants (1913-14), Taylor made his name playing for the team one of his brothers, C.I. Taylor, managed and owned, the Indianapolis ABCs.
+This polynomial sequence is of [[binomial type]]: conversely, every polynomial sequence of binomial type may be obtained from the Abel sequence in the [[umbral calculus]].
-Following a 1915 season in which he hit .308, he set Cuba ablaze, hitting .500 in winter league play. He took that hot bat into the 1916 championship season. Ben went 11-for-18 in the World Series, stealing three bases in five games.
+==References==
-Other than a 1919 season split between Hilldale and a managerial stint with the Bacharach Giants, Ben played with the ABCs from 1914 to 1922. In that final season, he replaced C.I. as manager, following his death.
+* {{cite journal | author=Gian-Carlo Rota | authorlink=Gian-Carlo Rota | coauthors=Jianhong Shen, Brian D. Taylor | title=All polynomials of binomial type are represented by Abel polynomials | journal=Annali della Scuola Normale Superiore di Pisa - Classe di Scienze Sér. 4 | volume=25 | issue=3-4 | year= 1997 | pages= 731-738 | url=http://www.numdam.org/item?id=ASNSP_1997_4_25_3-4_731_0 | accessdate=2008-07-26 }}
+==External links==
+* {{MathWorld | urlname=AbelPolynomial | title=Abel Polynomial}}
+[[Category:Polynomials]]
-In 1923, Taylor organized the Washington Potomacs, bringing brother Johnny along as pitching coach. The team joined the new Eastern Colored League in its inaugural season the following year.
-Defensively, he was good on ground balls and could execute all the plays at first, making the other infielders look good by digging out low throws and making difficult plays with such ease that they appeared routine.
-Always a heads-up players, Ben was an ideal man to have on a ball club. During his career, he was also a manager and excellent teacher of young players. It was from him that [[Buck Leonard]] learned to polish and refine his skills as a first baseman.
-Ben continued as a player/manager, joining Harrisburg in 1925 and the Baltimore Black Sox from 1926 to 1928. He was then traded to the Bacharach Giants in exchange for their manager Dick Lundy prior to the 1929 campaign, the final season of his playing career. He continued to coach and manage until 1940.
-After retiring, Taylor was an active businessman, operating a poolroom and acquiring the rights to print and sell game programs at [[Baltimore Elite Giants]] games.
-In 1952, as the Negro Leagues decline was in rapid motion, the [[Pittsburgh Courier]] polled its readers to name the greatest players of the Negro Leagues. They eventually named 5 teams plus honorable mentions. Among those honored, Taylor was awarded 2nd team, first base.
-He died at age 64 in [[Baltimore, Maryland]].
-He was the youngest of four brothers who all became famous in baseball, including [[C. I. Taylor|C.I.]], [[Candy Jim Taylor|Candy Jim]] and [[Johnny Taylor (baseball)|Johnny]] ("Steel Arm").
-==References==
-*[http://www.baseballhalloffame.org/hofers/detail.jsp?playerId=506639 Baseball Hall of Fame bio]
-*[http://www.findagrave.com/cgi-bin/fg.cgi?page=gr&GRid=20713 Find-A-Grave bio]
+{{algebra-stub}}
-{{2006 Baseball HOF}}
-{{Baseball Hall of Fame first basemen}}
+[[eo:Abela polinomo]]
-{{DEFAULTSORT:Taylor, Ben}}
+[[fr:Polynôme d'Abel]]
-[[Category:National Baseball Hall of Fame inductees]]
+[[km:ពហុធាអាបែល]]
-[[Category:Negro league baseball players]]
-[[Category:Negro league baseball managers]]
-[[Category:1888 births]]
-[[Category:1953 deaths]]