in this paper, an integration of a symbolic power series method - padé approximation technique (ps - padé), was utilized to solve a system of nonlinear differential equations arising from the similarity solution of laminar thermal boundary layer over a flat plate subjected to a convective surface boundary condition. as both boundary conditions tended to infinity, the combination of series solut...

we need sociology theories, for that understand of sociology and politic problems. french sociologist pierre bourdieu's theory practice and symbolic power are our best resource; for understanding social and political fields. this article reviews the language and symbolic power; indicating its function in social and political fields. we need sociology theories, for that understand of sociol...

Let f∗(z) = ∞ ∑ j=0 aj z j be a convergent series in which {aj}j=0 are known real numbers. In this paper, by referring to Osler’s lemma [8], we obtain explicit forms of the two bivariate series ∞ ∑ j=0 an j+m r j cos(α+ j)θ and ∞ ∑ j=0 an j+m r j sin(α+ j)θ, where r, θ are real variables, α ∈ R, n ∈ N and m ∈ {0, 1, . . . , n − 1}. With some illustrative examples, we also show how to obtain the...

let $k$ be a field of characteristic$p>0$, $k[[x]]$, the ring of formal power series over $ k$,$k((x))$, the quotient field of $ k[[x]]$, and $ k(x)$ the fieldof rational functions over $k$. we shall give somecharacterizations of an algebraic function $fin k((x))$ over $k$.let $l$ be a field of characteristic zero. the power series $finl[[x]]$ is called differentially algebraic, if it satisfies...

A term an is m-fold hypergeometric, for a given positive integer m, if the ratio $${{a}_{{n + m}}}{\text{/}}{{a}_{n}}$$ rational function over field $$\mathbb{K}$$ of characteristic zero. We establish structure holonomic recurrence equations, i.e. linear and homogeneous equations having polynomial coefficients, that have hypergeometric solutions , any m. Consequently, we describe new algorithm,...

In this paper, an integration of a symbolic power series method - Padé approximation technique (PS - Padé), was utilized to solve a system of nonlinear differential equations arising from the similarity solution of laminar thermal boundary layer over a flat plate subjected to a convective surface boundary condition. As both boundary conditions tended to infinity, the combination of series solut...