Q-Charlier polynomials

2022-05-14T06:55:39Z

2A02:C7D:F025:9900:3581:4053:95B7:4A4A: Removed empty sections

{{DISPLAYTITLE:''q''-Charlier polynomials }}
In mathematics, the '''''q''-Charlier polynomials'''<ref>There are similar named polynomials named alternative q-Charlier polynomials <math>K_n(x;a;q)</math> which is another name for q-Bessel polynomials.</ref> are a family of basic hypergeometric [[orthogonal polynomials]] in the basic [[Askey scheme]]. {{harvs|txt | last1=Koekoek | first1=Roelof | last2=Lesky | first2=Peter A. | last3=Swarttouw | first3=René F. | title=Hypergeometric orthogonal polynomials and their q-analogues | publisher=[[Springer-Verlag]] | location=Berlin, New York | series=Springer Monographs in Mathematics | isbn=978-3-642-05013-8 | doi=10.1007/978-3-642-05014-5 | mr=2656096 | year=2010|loc=14}} give a detailed list of their properties.

==Definition==

The polynomials are given in terms of the [[basic hypergeometric function]] by
:<math>\displaystyle C_n(q^{-x};a;q) = {}_2\phi_1(q^{-n},q^{-x};0;q,-q^{n+1}/a).</math>

==References==
{{Reflist}}

*{{Citation | last1=Gasper | first1=George | last2=Rahman | first2=Mizan | title=Basic hypergeometric series | publisher=[[Cambridge University Press]] | edition=2nd | series=Encyclopedia of Mathematics and its Applications | isbn=978-0-521-83357-8 | doi=10.2277/0521833574 | mr=2128719 | year=2004 | volume=96}}
*{{Citation | last1=Koekoek | first1=Roelof | last2=Lesky | first2=Peter A. | last3=Swarttouw | first3=René F. | title=Hypergeometric orthogonal polynomials and their q-analogues | publisher=[[Springer-Verlag]] | location=Berlin, New York | series=Springer Monographs in Mathematics | isbn=978-3-642-05013-8 | doi=10.1007/978-3-642-05014-5 | mr=2656096 | year=2010}}
*{{dlmf|id=18|title=Chapter 18: Orthogonal Polynomials|first=Tom H. |last=Koornwinder|first2=Roderick S. C.|last2= Wong|first3=Roelof |last3=Koekoek||first4=René F. |last4=Swarttouw}}
*{{cite thesis |last=Sadjang |first=Patrick Njionou |title=Moments of Classical Orthogonal Polynomials |type=Ph.D. |publisher=Universität Kassel |url=https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.643.3896&rep=rep1&type=pdf |access-date=February 21, 2021}}

[[Category:Orthogonal polynomials]]
[[Category:Q-analogs]]
[[Category:Special hypergeometric functions]]

Archive:Wasta

2017-01-23T22:26:34Z

2A02:C7D:5054:FE00:89F4:74D7:8A75:5544: Grammar

{{for|the town in the United States|Wasta, South Dakota}}
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'''Wasta''' or '''wasata''' (Arabic: وَاسِطة ''wāsiṭah'') is an Arabic word that loosely translates into [[nepotism]], '[[Wiktionary:clout#Noun|clout]]' or 'who you know'. It refers to using one’s connections and/or influence to get things done, including government transactions such as the quick renewal of a passport, waiving of traffic fines, and getting hired for or promoted in a job.

In other words, it amounts to getting something through favoritism rather than merit, or what is informally spoken of in English as "pull" from connections (the opposite of "push"). The English word [[cronyism]] overlaps in meaning but is not precisely the same. Roughly equivalent words in other languages include [[sociolismo]] in Cuba; [[Blat (Russia)|blat]] in Russia; [[guanxi]] in Chinese and ''Vetternwirtschaft'' in German, ''protektzia'' in Israeli slang, ''un pituto'' in Chilean Spanish, In Brazilian-Portuguese it is referred to as "pistolão", "QI" (''Quem Indica'', or Who Indicates), or in the slang "peixada", "Pidi Padu" in [[Malayalam]], "arka" or "destek" in Turkish, "plecy" in Polish.

==Etymology==
Wasta is derived from the Modern Standard [[Arabic]] word وَاسِطَة (''wāsiṭah'') which can mean ''medium, means'' but also ''personal connection used to gain something''.<ref>Hans Wehr (1979), ''Arabic-English Dictionary''.</ref> In Hindi, Wasta means "Concern".

Furthermore, companies in the [[Arab world]] rarely have a 'no-[[nepotism]]' policy in place, so one can often find a workforce with friends and friends relatives who may or may not be qualified. This takes place in both the public and private sectors.

In many Arab countries, such as [[Oman]], [[Iraq]], [[Lebanon]], [[Kuwait]], [[UAE]], [[Saudi Arabia]] and [[Jordan]], wasta affects hiring and promotion decisions. This is not restricted to Arab nationals but is also practised by expatriates who use their connections as wastas.

With respect to recruitment, there seems to be a movement away from this wasta, especially in the case of multinationals and professional firms. However, Wasta is still widely used in the region.

==See also==
* {{Portal-inline|Middle East}}

==Notes==
<references/>

==Bibliography==
* Regulation, Trust, and Cronyism in Middle Eastern Societies: The Simple Economics of 'Wasta'. (2011) Andy H. Barnett, Bruce Yandle, George Naufal, School of Business and Management-American University of Sharjah, Department of Economics- Clemson University, School of Business and Management- American University of Sharjah.
* Hutchings, K. & Weir, D. (2006).Guanxi and Wasta: A comparison. Thunderbird International Business Review, 48(1), 141-156
* Izraeli, D. (1997). Business Ethics in the Middle East. Journal of Business Ethics, 16(14), 1555-1560
* Kocherlakota, N. R. (1996). Money is Memory. Federal Reserve Bank of Minneapolis, Research Department Staff Report 218, 1-37

[[Category:Nepotism]]
[[Category:Arab culture]]
[[Category:Pakistani culture]]
[[Category:Pakistani social culture]]

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Q-Charlier polynomials

Archive:Wasta