The gamma function via interpolation

Causley, Matthew F.

doi:10.1007/s11075-021-01204-8

Cited by 1 publication

(1 citation statement)

References 32 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…From this trend we mention [40] (improving on Ramanujan) and [18] (improving on Windschitl), with [83] presenting the latest Windschitl variations, while [56] is more on reviewing/comparisons. All those exhibiting higher accuracies and speeds (of convergence) seem to be trading these for more and more cumbersome formulas (see [16,45,46,65]).…”

Section: Gamma Functionmentioning

confidence: 99%

Approximating the Level Curves on Pascal’s Surface

Dăuş

Jianu

Nagy

et al. 2022

INT J COMPUT COMMUN, Int. J. Comput. Commun. Control

View full text Add to dashboard Cite

It is well-known that in general the algorithms for determining the reliability polynomial associated to a two-terminal network are computationally demanding, and even just bounding the coefficients can be taxing. Obviously, reliability polynomials can be expressed in Bernstein form, hence all the coefficients of such polynomials are fractions of the binomial coefficients. That is why we have very recently envisaged using an extension of the classical discrete Pascal’s triangle (which comprises all the binomial coefficients) to a continuous version/surface. The fact that this continuous Pascal’s surface has real values in between the binomial coefficients makes it appealing as being a mathematical concept encompassing all the coefficients of all the reliability polynomials (which are integers, as resulting from counting processes) and more. This means that, the coefficients of any reliability polynomial can be represented as discrete steps (on level curves of integer values) on Pascal’s surface. The equation of this surface was formulated by means of the gamma function, for which quite a few approximation formulas are known. Therefore, we have started by reviewing many of those results, and have used a selection of those approximations for the level curves problem on Pascal’s surface. Towards the end, we present fresh simulations supporting the claim that some of these could be quite useful, as being both (reasonably) easy to calculate as well as fairly accurate.

show abstract