We define a new class of generating function transformations related to polylogarithm functions, Dirichlet series, and Euler sums. These transformations are given by an infinite sum over the jth derivatives of a sequence generating function and sets of generalized coefficients satisfying a non-triangular recurrence relation in two variables. The generalized transformation coefficients share a n...

In this paper, we consider some properties such as growth and distortion theorem, coefficient problems, linear combinations for certain subclass of meromorphic harmonic functions with positive coefficients.

We present several polynomial congruences about sums with central binomial coefficients and harmonic numbers. In the final section we collect some new congruences involving Fibonacci and Lucas numbers.

Background Leaf shape among Passiflora species is spectacularly diverse. Underlying this diversity in leaf shape are profound changes in the patterning of the primary vasculature and laminar outgrowth. Each of these aspects of leaf morphology-vasculature and blade-provides different insights into leaf patterning. Results Here, we morphometrically analyze >3300 leaves from 40 different Passifl...

The diffusion coefficients at control volume surfaces are required in the most-widely used finite-volume method for numerical simulation of convection-diffusion equations. Various interpolation methods for diffusion coefficients at control volume surfaces are briefly discussed and extensively compared with the analytical solutions of both pure diffusion and convection-diffusion problems in this...

We evaluate the virial coefficients Bk for k ≤ 10 for hard spheres in dimensions D = 2, · · · , 8. Virial coefficients with k even are found to be negative when D ≥ 5. This provides strong evidence that the leading singularity for the virial series lies away from the positive real axis when D ≥ 5. Further analysis provides evidence that negative virial coefficients will be seen for some k > 10 ...

Background Leaf shape among Passiflora species is spectacularly diverse. Underlying this diversity in leaf shape are profound changes in the patterning of the primary vasculature and laminar outgrowth. Each of these aspects of leaf morphology-vasculature and blade-provides different insights into leaf patterning. Results Here, we morphometrically analyze >3300 leaves from 40 different Passifl...