On q-series and continued fractions

In this paper we have established interesting results involving continued fraction. Special cases of the result established herein have also been discussed

Wavelet Analysis on the Sphere

The goal of this monograph is to develop the theory of wavelet harmonic analysis on the sphere. By starting with orthogonal polynomials and functional Hilbert spaces on the sphere, the foundations are laid for the study of spherical harmonics such as zonal functions. The book also discusses the construction of wavelet bases using special functions, especially Bessel, Hermite, Tchebychev, and Gegenbauer polynomials

Geometrical Theory of Analytic Functions

The book contains papers published in the Mathematics Special Issue, entitled "Geometrical Theory of Analytic Functions". Fifteen papers devoted to the study concerning complex-valued functions of one variable present new outcomes related to special classes of univalent functions, differential equations in view of geometric function theory, quantum calculus and its applications in geometric function theory, operators and special functions associated with differential subordination and superordination theories and starlikeness, and convexity criteria

The origin of dwarf carbon stars

Dwarf carbon (dC) stars are low-mass, main-sequence stars that exhibit spectra analogous to carbon-rich giants found along the asymptotic giant branch. An almost half a century old hypothesis postulates that the peculiar atmospheric chemistry of dC stars is owed to mass transfer from an evolved companion. Speci cally, while the former primary ascended the asymptotic giant branch, triple- -processed material was dredged to the surface before the stellar wind liberated the carbon-enhanced outer layers. The liberated material is then transferred to the main-sequence companion, polluting its atmosphere, and forming a dC star, while the original primary becomes a white dwarf. In this thesis, I present the results of a decade-long spectroscopic survey of 37 dC stars to test this binary evolution hypothesis. Using MCMC simulations to analyse the radial-velocity variations of all 37 dC stars in this sample, it has been possible to show that the population is consistent with a 100 per cent binary fraction and are thus likely the product of mass transfer. Furthermore, the orbital parameters of nine dC stars are reported for the rst time, increasing the number of known dC binaries by 220 per cent. Interestingly, eight of these newly constrained dC binaries exhibit emission features in their optical spectrum. Moreover, the orbital periods of these emission-line dC stars are all shorter than 12 d, implying that these stars have evolved through a common envelope. Thus, the discovery of eight short-orbital period dC stars indicates that low-mass, metal-weak or metal-poor stars can accrete substantial material before entering the common-envelope phase. Finally, a kinematical study of 1200 candidate dC stars is presented, with the analysis indicating that as much as 70 per cent of the population may possess Galactic orbits that are inconsistent with thin disc membership. This result, therefore, suggests that dC stars are generally old and likely metal-poor

Continued fractions for Rogers-Szegö polynomials

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