Name
Abstract | ||
|---|---|---|
In this paper, by using the extended Sturm-Liouville theorem for symmetric functions, we introduce the differential equation @F"n^''(t)+((n+a(1-(-1)^n)/2)^2-a(a+1)cos^2t(1-(-1)^n)/2)@F"n(t)=0, as a generalization of the differential equation of trigonometric sequences {sinnt}"n"="1^~ and {cosnt}"n"="0^~ for a=0 and obtain its explicit solution in a simple trigonometric form. We then prove that the obtained sequence of solutions is orthogonal with respect to the constant weight function on [0,@p] and compute its norm square value explicitly. One of the important advantages of this generalization is to find some new infinite series. A practical example is given in this sense. |
Year | DOI | Venue |
|---|---|---|
2008 | 10.1016/j.camwa.2008.07.023 | Computers & Mathematics with Applications |
Keywords | Field | DocType |
trigonometric sequence,practical example,simple trigonometric form,differential equation,symmetric orthogonal functions,extended sturm–liouville theorem for symmetric functions,important advantage,constant weight function,new infinite series,extended sturm-liouville theorem,fourier trigonometric series,norm square value,explicit solution,fourier trigonometric sequences,hypergeometric functions,weight function,hypergeometric function,sturm liouville,infinite series,symmetric function | Trigonometric series,Differential equation,Trigonometric polynomial,Proofs of trigonometric identities,Symmetric function,Weight function,Trigonometric functions,Series (mathematics),Mathematical analysis,Mathematics | Journal |
Volume | Issue | ISSN |
56 | 11 | Computers and Mathematics with Applications |
Citations | PageRank | References |
2 | 0.72 | 0 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Mohammad Masjed-Jamei | 1 | 15 | 8.03 |
| Mehdi Dehghan | 2 | 3022 | 324.48 |