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Open AccessEditorial

An Introductory Overview of Bessel Polynomials, the Generalized Bessel Polynomials and the q-Bessel Polynomials

by Hari Mohan Srivastava

Symmetry 2023, 15(4), 822; https://doi.org/10.3390/sym15040822 - 29 Mar 2023

Cited by 45 | Viewed by 6733

Named essentially after their close relationship with the modified Bessel function

K_{ν} (z)

of the second kind, which is known also as the Macdonald function (or, with a slightly different definition, the Basset function), the so-called Bessel polynomials [...] Read more.

Named essentially after their close relationship with the modified Bessel function

K_{ν} (z)

of the second kind, which is known also as the Macdonald function (or, with a slightly different definition, the Basset function), the so-called Bessel polynomials

y_{n} (x)

and the generalized Bessel polynomials

y_{n} (x; α, β)

stemmed naturally in some systematic investigations of the classical wave equation in spherical polar coordinates. Our main purpose in this invited survey-cum-expository review article is to present an introductory overview of the Bessel polynomials

y_{n} (x)

and the generalized Bessel polynomials

y_{n} (x; α, β)

involving the asymmetric parameters

α

and

β

. Each of these polynomial systems, as well as their reversed forms

θ_{n} (x)

and

θ_{n} (x; α, β)

, has been widely and extensively investigated and applied in the existing literature on the subject. We also briefly consider some recent developments based upon the basic (or quantum or q-) extensions of the Bessel polynomials. Several general families of hypergeometric polynomials, which are actually the truncated or terminating forms of the series representing the generalized hypergeometric function

_{r} F_{s}

with r symmetric numerator parameters and s symmetric denominator parameters, are also investigated, together with the corresponding basic (or quantum or q-) hypergeometric functions and the basic (or quantum or q-) hypergeometric polynomials associated with

_{r} Φ_{s}

which also involves r symmetric numerator parameters and s symmetric denominator parameters. Full article

(This article belongs to the Section C: Physics)

12 pages, 343 KB

Open AccessArticle

Blue Sublime and the Time of Capital

by Filippo Menozzi

Humanities 2020, 9(3), 73; https://doi.org/10.3390/h9030073 - 4 Aug 2020

Cited by 2 | Viewed by 4340

Abstract

This essay proposes a concept of the “blue sublime” in order to address how the contradictions of capitalist accumulation regimes manifest themselves in the hydrosphere. My argument starts from the fact that capitalism entails a shift in the imagination of the sea: from the point of view of commodity production and consumption, the sea has turned into field of extraction, resource to be exploited or waste disposal site. But capitalism also involves circulation, which casts the sea into a space of contradictions. On the one hand, the oceanic expanse can be an image for the flow of capital and commodities, and a privileged route that has been central to the mercantile expansion of the world economy. On the other hand, however, the sea can become the emblem of the limit to accumulation, and the ultimate barrier to capital’s self-expansion. The blue sublime, hence, provides an image for picturing the totality of capitalism, while in its materiality it embodies capitalism’s contingency and perishability. From this point of view, the blue sublime registers a process described by Marx as the “annihilation of space by time” proper to the universalizing tendency of capital. Through a reading of Marx’s Grundrisse, the blue sublime hence provides a tangible representation of the asymptotic tendency of capital to reach a zero time of circulation and a privileged location to grasp the material contradictions of a global modernity. Full article

(This article belongs to the Special Issue World Literature and the Blue Humanities)

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