Favard's theorem: Difference between revisions

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{{distinguish|Al-Salam–Chihara polynomials}}
In mathematics, '''Al-Salam–Carlitz polynomials''' ''U''{{su|b=''n''|p=(''a'')}}(''x'';''q'') and ''V''{{su|b=''n''|p=(''a'')}}(''x'';''q'') are two families of basic hypergeometric [[orthogonal polynomials]] in the basic [[Askey scheme]], introduced by {{harvs|txt|last=Al-Salam|authorlink=Waleed Al-Salam|last2=Carlitz|author2-link=Leonard Carlitz|year=1965}}. {{harvs|txt | last1=Koekoek | first1=Roelof | last2=Lesky | first2=Peter A. | last3=Swarttouw | first3=René F. | title=Hypergeometric orthogonal polynomials and their q-analogues | doi=10.1007/978-3-642-05014-5 | 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=14.24, 14.25}} give a detailed list of their properties.
 
==Definition==
 
The Al-Salam–Chihara polynomials are given in terms of [[basic hypergeometric function]]s by
:<math> U_n^{(a)}(x;q) = (-a)^nq^{n(n-1)/2}{}_2\phi_1(q^{-n}, x^{-1};0;q,qx/a)</math>
:<math> V_n^{(a)}(x;q) = (-a)^nq^{-n(n-1)/2}{}_2\phi_0(q^{-n}, x;;q,q^n/a)</math>
 
==References==
 
*{{Citation | last1=Al-Salam | first1=W. A. | last2=Carlitz | first2=L. | author2-link=Leonard_Carlitz | title=Some orthogonal q-polynomials | doi=10.1002/mana.19650300105 | mr=0197804 | year=1965 | journal=[[Mathematische Nachrichten]] | issn=0025-584X | volume=30 | pages=47–61}}
*{{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}}
 
{{DEFAULTSORT:Al-Salam-Carlitz polynomials}}
[[Category:Orthogonal polynomials]]

Revision as of 15:17, 1 April 2013

Template:Distinguish In mathematics, Al-Salam–Carlitz polynomials UTemplate:Su(x;q) and VTemplate:Su(x;q) are two families of basic hypergeometric orthogonal polynomials in the basic Askey scheme, introduced by Template:Harvs. Template:Harvs give a detailed list of their properties.

Definition

The Al-Salam–Chihara polynomials are given in terms of basic hypergeometric functions by

Un(a)(x;q)=(a)nqn(n1)/22ϕ1(qn,x1;0;q,qx/a)
Vn(a)(x;q)=(a)nqn(n1)/22ϕ0(qn,x;;q,qn/a)

References

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    Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

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    Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

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    15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

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