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We analyze the polynomial solutions of the linear differential equation where is a -degree polynomial. We discuss all the possible polynomial solutions and their dependence on the parameters of the polynomials . Special cases are related to known differential equations of mathematical physics. Class...
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The one-dimensional Schr ̈odinger’s equation is analysed w ith regard to the existence of exact solutions for decatic polynomial potentials. Under c ertain conditions on the potential’s pa- rameters, we show that the decatic polynomial potential V ( x ) = ax 10 + bx 8 + cx 6 + dx 4 + ex 2 , a >...
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Analytic evaluation of Gordon's integral Jj(±p)c(b,b′;λ,w,z)=∫∞0xc+j−1e−λx1F1(b;c;wx)1F1(b′;c±p;zx)dx, are given along with convergence conditions. It shows enormous number of definite integrals, frequently appear in theoretical and mathematical physics applications, easily ded...
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Using the orthonormality of the 2D-Zernike polynomials reproducing kernels, reproducing kernel Hilbert spaces and ensuing coherent states are attained. With the aid of the so obtained coherent states the complex unit disc is quantized. Associated upper symbols, lower symbols and related generalized ...
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We survey the theory of square integrable group representations for the non-compact, semisimple lie group SU(1,1), which has three different series of representations: principal, complementary and discrete. As a result of our survey we conclude that the discrete series representations are the only o...
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