Analytic structure of the associated Legendre functions of the second kind
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DOI: 10.1063/5.0142253
Abstract: We consider the complex ν plane structure of the associated Legendre functions of the second kind Qν−1/2−K(coshρ). We find that for any noninteger value of K the Qν−1/2−K(coshρ) have an infinite number of poles in… read more here.
Keywords: number; exceptional points; associated legendre; functions second ... See more keywords
Orthogonality of the Ferrers' associated Legendre functions of the second kind with imaginary argument
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DOI: 10.1080/10652469.2017.1322965
Abstract: ABSTRACT In this work we study the associated Legendre functions of the second kind with a purely imaginary argument . We derive the conditions under which they provide a set of square integrable functions when… read more here.
Keywords: second kind; imaginary argument; legendre functions; functions second ... See more keywords
Some New Boole-Type Inequalities via Modified Convex Functions with Their Applications and Computational Analysis
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DOI: 10.3390/math13213517
Abstract: In numerical analysis, the Boole’s formula serves as a pivotal tool for approximating definite integrals. The approximation of the definite integrals has a big role in numerical methods for differential equations; in particular, in the… read more here.
Keywords: analysis; functions second; computational analysis; convex functions ... See more keywords