Continued Fractions for Special Functions: Handbook and Software

Cuyt, Annie; Backeljauw, Franky; Becuwe, Stefan; Colman, Michel; Docx, Tom; Deun, Joris Van

doi:10.1007/978-3-642-01591-5_3

Cited by 18 publications

(27 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Substituting this expression in Eq. ͑17͒ and using the Jacobi-Anger expansion 22 of the exponential functions in series of Bessel functions J n ͑ ͒ of the first kind of integer order m,…”

Section: Appendix Amentioning

confidence: 99%

X-ray cross-correlation analysis and local symmetries of disordered systems: General theory

2010

View full text Add to dashboard Cite

In a recent paper ͓P. Wochner et al., Proc. Natl. Acad. Sci. U.S.A. 106, 11511 ͑2009͔͒ x-ray scattering intensity correlations around a ring, in the speckle diffraction pattern of a colloidal glass, were shown to display a remarkable ϳcos͑n ͒ dependence on the angular coordinate around the ring, with integer index n depending on the magnitude of the scattering wave vector. With an analytical derivation that preserves full generality in the Fraunhofer diffraction limit, we clarify the relationship between this result and previous x-ray studies of bond-orientation order, and provide a sound basis to the statement that the angular intensity correlations deliver information on local bond arrangements in a disordered ͑or partially ordered͒ system. We present a detailed analysis of the angular cross-correlation function and show its applicability for studies of a wide range of structural properties of disordered systems, from local structure to spatial correlations between distant structural elements.

show abstract

Section: Appendix Amentioning

confidence: 99%

X-ray cross-correlation analysis and local symmetries of disordered systems: General theory

2010

View full text Add to dashboard Cite

show abstract

“…where 0 F 1 2; jr 2 À Á 2 is the confluent hypergeometric limit function, which is defined as [30,31] …”

Section: Semi-analytical Solutionmentioning

confidence: 99%

Analytical and numerical study of the electro-osmotic annular flow of viscoelastic fluids

Ferrás

Afonso

Alves

et al. 2014

Journal of Colloid and Interface Science

View full text Add to dashboard Cite

a b s t r a c tIn this work we present semi-analytical solutions for the electro-osmotic annular flow of viscoelastic fluids modeled by the Linear and Exponential PTT models. The viscoelastic fluid flows in the axial direction between two concentric cylinders under the combined influences of electrokinetic and pressure forcings. The analysis invokes the Debye-Hückel approximation and includes the limit case of pure electro-osmotic flow. The solution is valid for both no slip and slip velocity at the walls and the chosen slip boundary condition is the linear Navier slip velocity model. The combined effects of fluid rheology, electro-osmotic and pressure gradient forcings on the fluid velocity distribution are also discussed.

show abstract

“…The class D is quite wide since it covers almost all of the examples given in the book [3] which comprises with lot of CF expansions of very known mathematical constants, as well as elementary and special functions; see Part III of the book. It does not cover only the subclass of so-called q-CFs, where the numerators and denominators a n , a n , b n , b n (cf.…”

Section: Class Dmentioning

confidence: 99%

“…It does not cover only the subclass of so-called q-CFs, where the numerators and denominators a n , a n , b n , b n (cf. (2)) are expressed in terms of q n (see, e.g., [3,Section 19]). One can also find some applications of k-variant CFs ∈ D with k > 2 (see, e.g., [3,p.…”

Section: Class Dmentioning

confidence: 99%