Analytic stage–discharge formulae are derived for flow in straight trapezoidal channels, based on the 2D analytic velocity distribution in open channels given by Shiono and Knight [Shiono K, Knight DW, Turbulent open-channel flows with variable depth across the channel. J Fluid Mech 1991;222:...
Here, we use a similar methodological and conceptual approach to examine complexity in another exemplary model system, the vertebral column of mammals28,29,30, although other serial structures (for example, body segments, paired appendages and teeth) would be suitable in other groups (for example,...
start with r and increase by 1 until reached r = n At most start with r and decrease by 1 until reached r = 0 Binomial Expansion (find a specific term) ₙCᵣ (a)ⁿ⁻ʳ (b)ʳ, r is one less than the term needed
Transformation formulae for multivariable basic hypergeometric series 文档格式: .pdf 文档大小: 214.43K 文档页数: 16页 顶/踩数: 0/0 收藏人数: 0 评论次数: 0 文档热度: 文档分类: 待分类 文档标签: Transformationformulaeformultivariablebasichypergeometricseries ...
Rothe formulaeBy means of the classical Lagrange expansion theorem, five convolution formulae are established for the orthogonal polynomials named after Laguerre, Jacobi, Meixner, Gegenbauer and Pollaczek, that contain the well-known Hagen–Rothe formula for binomial coefficients as common special case...
Analytic stage–discharge formulae are derived for flow in straight trapezoidal channels, based on the 2D analytic velocity distribution in open channels given by Shiono and Knight [Shiono K, Knight DW, Turbulent open-channel flows with variable depth across the channel. J Fluid Mech 1991;222:...
By establishing new multiple inverse series relations (with their connection coefficients being given by higher derivatives of fixed multivariate analytic functions), we illustrate a general framework to provide new proofs for MacMahon’s master theorem and the multivariate expansion formula due to Good ...