Asymptotic Properties of Derivatives of the Stieltjes Polynomials
Let 𝑤𝜆(𝑥)∶=(1−𝑥2)𝜆−1/2 and 𝑃𝜆,𝑛(𝑥) be the ultraspherical polynomials with respect to 𝑤𝜆(𝑥). Then, we denote the Stieltjes polynomials with respect to 𝑤𝜆(𝑥) by 𝐸𝜆,𝑛+1(𝑥) satisfying ∫1−1𝑤𝜆(𝑥)𝑃𝜆,𝑛(𝑥)𝐸𝜆,𝑛+1(𝑥)𝑥𝑚𝑑𝑥=0, 0≤𝑚<𝑛+1, ∫1−1𝑤𝜆(𝑥)𝑃𝜆,𝑛(𝑥)𝐸𝜆,𝑛+1(𝑥)𝑥𝑚𝑑𝑥≠0, 𝑚=𝑛+1. In this paper, we investigate asymp...
| প্রধান লেখক: | , |
|---|---|
| বিন্যাস: | প্রবন্ধ |
| ভাষা: | English |
| প্রকাশিত: |
Hindawi Limited
2012-01-01
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| মালা: | Journal of Applied Mathematics |
| অনলাইন ব্যবহার করুন: | http://dx.doi.org/10.1155/2012/482935 |