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Definite integrals involving Whittaker functions
Mathematical Proceedings of the Cambridge Philosophical Society, 1968Little is known about definite integrals for the Whittaker functions. The object of this paper is to establish such results and the following formulae are establishedwhere the symbol means that in the expression following it i is to be replaced by –i and the two expressions are to be added.
Ragab, F. M., Simary, M. A.
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Expansions of generalized Whittaker functions
Mathematical Proceedings of the Cambridge Philosophical Society, 1954ABSTRACTIn this paper I give a direct proof of a new expansion of the Whittaker function M(a; b; x) as a series of Bessel functions, and some generalizations of this result for the functions 2F2(x) and 4F4(x).
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An Infinite Order Whittaker Function
Canadian Journal of Mathematics, 2009Abstract. In this paper we construct a flat smooth section of an induced space I(s, η) of SL2(ℝ) so that the attached Whittaker function is not of finite order. An asymptotic method of classical analysis is used.
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Expansions of certain Whittaker functions
Mathematical Proceedings of the Cambridge Philosophical Society, 1960ABSTRACTAn expansion of the Whittaker function Wk, m(z) in terms of Bessel functions is given for 2m an integer or zero. Simple formulae are derived for the cases of m = 0, ½, 1 and . The case m = 0 provides expansions for the exponential, sine, cosine and similar integrals.
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Composition and functions of bacterial membrane vesicles
Nature Reviews Microbiology, 2023Masanori Toyofuku +2 more
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Gene regulation by long non-coding RNAs and its biological functions
Nature Reviews Molecular Cell Biology, 2020Luisa Statello +2 more
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The expanding regulatory mechanisms and cellular functions of circular RNAs
Nature Reviews Molecular Cell Biology, 2020Ling-Ling Chen
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Risk assessment of microplastic particles
Nature Reviews Materials, 2022Albert A Koelmans +2 more
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