| Abstrakt: |
This paper deals with transmutation theory and how we can use the integral transforms composition method (ITCM) to develop generalized transmutation operators. With the ITCM, we can create various transmutation operators by combining different integral transforms like Hankel, Y, Mellin, Laplace, and Fourier, sine- and cosine-Fourier, and other generalized transforms. The paper applies the ITCM to derive connection formulas for solutions of both singular and nonsingular differential equations. It concludes that using the ITCM to construct transmutations is a valuable and practical approach for finding connection formulas and explicit solutions for a wide range of differential equations, including those with Bessel operators. [ABSTRACT FROM AUTHOR] |
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