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{{about||the orthogonal polynomials|Stieltjes-Wigert polynomial|the polynomials associated to a family of orthogonal polynomials|Stieltjes polynomials}}


In mathematics, the '''Heine–Stieltjes polynomials''' or '''Stieltjes polynomials''', introduced by {{harvs|txt|authorlink=T. J. Stieltjes|first=T. J. |last=Stieltjes|year=1885}}, are polynomial solutions of a second-order [[Fuchsian equation]], a [[differential equation]] all of whose singularities are [[regular singularity|regular]].  The Fuchsian equation has the form


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:<math>\frac{d^2 S}{dz^2}+\left(\sum _{j=1}^N \frac{\gamma _j}{z - a_j} \right) \frac{dS}{dz} + \frac{V(z)}{\prod _{j=1}^N (z - a_j)}S = 0</math>
 
for some polynomial ''V''(''z'') of degree at most ''N''&nbsp;&minus;&nbsp;2, and if this has a polynomial solution ''S'' then ''V'' is called a Van Vleck polynomial (after [[Edward Burr Van Vleck]]) and ''S'' is called a Heine–Stieltjes polynomial.
 
[[Heun polynomial]]s are the special cases of Stieltjes polynomials when the differential equation has four singular points.
 
==References==
*{{Citation | last1=Marden | first1=Morris | title=On Stieltjes Polynomials | jstor=1989516 | publisher=[[American Mathematical Society]] | location=Providence, R.I. | year=1931 | journal=[[Transactions of the American Mathematical Society]] | issn=0002-9947 | volume=33 | issue=4 | pages=934–944}}
*{{dlmf|id=31.15|title=Stieltjes Polynomials|first=B. D.|last=Sleeman|first2=V. B. |last2=Kuznetzov}}
*{{Citation | last1=Stieltjes | first1=T. J. | title= Sur certains polynômes qui vérifient une équation différentielle linéaire du second ordre et sur la theorie des fonctions de Lamé  | doi=10.1007/BF02400421 | year=1885 | journal= Acta Mathematica | volume=6 | issue=1 | pages=321–326}}
 
{{DEFAULTSORT:Heine-Stieltjes polynomials}}
[[Category:Polynomials]]

Latest revision as of 15:16, 14 December 2013

29 yr old Orthopaedic Surgeon Grippo from Saint-Paul, spends time with interests including model railways, top property developers in singapore developers in singapore and dolls. Finished a cruise ship experience that included passing by Runic Stones and Church.

In mathematics, the Heine–Stieltjes polynomials or Stieltjes polynomials, introduced by Template:Harvs, are polynomial solutions of a second-order Fuchsian equation, a differential equation all of whose singularities are regular. The Fuchsian equation has the form

for some polynomial V(z) of degree at most N − 2, and if this has a polynomial solution S then V is called a Van Vleck polynomial (after Edward Burr Van Vleck) and S is called a Heine–Stieltjes polynomial.

Heun polynomials are the special cases of Stieltjes polynomials when the differential equation has four singular points.

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

    Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

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