This equation becomes Wallis’ product when p = 0 and Vieta’s formula as p → ∞. It is surprising that such a connection between the two products was not discovered earlier. The collection [1] contains both original papers of Vieta and Wallis as well as other fundamental papers in the history of π. Indeed, there are many good historical sources on π. The text by P. Eymard and J. P. Lafon [6] is a...

We present a family of four-point quadrature rule, a generalization of Gauss-two point, Simpson’s 3/8, and Lobatto four-point quadrature rule for twice-differentiable mapping. Moreover, it is shown that the corresponding optimal quadrature formula presents better estimate in the context of four-point quadrature formulae of closed type. A unified treatment of error inequalities for different cla...

background: date (phoenix dactylifera l.) is one of the most important agricultural crops in iran. this study was carried out to determine the possibility of using date paste for manufacturing a new ready-to-eat food product. methods: various formulations were prepared by mixing mazafati date paste, bread, oil (animal and olive), nuts and spices but only six formulas were chosen according to se...

We introduce a new family of multiple orthogonal polynomials satisfying orthogonality conditions with respect to two weights $(w_1,w_2)$ on the positive real line, $w_1(x)=x^\alpha e^{-x}$ gamma density and $w_2(x) = x^\alpha E_{\nu+1}(x)$ related exponential integral $E_{\nu+1}$. give explicit formulas for type I functions II polynomials, their Mellin transform, Rodrigues formulas, hypergeomet...

The Langlands functoriality conjecture, as reformulated in the “beyond endoscopy” program, predicts comparisons between (stable) trace formulas of different groups G1,G2 for every morphism G1L→LG2 their L-groups. This conjecture can be seen a special case more general which replaces reductive by spherical varieties and formula its generalization, relative formula. goal this article precursor [1...