Journal of Computational and Applied Mathematics
A basic class of symmetric orthogonal functions with six free parameters
Journal of Computational and Applied Mathematics
Convergence tests on constant Dirichlet series
Computers & Mathematics with Applications
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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.