Padé approximant related to the Wallis formula
AbstractBased on the Padé approximation method, in this paper we determine the coefficients aj$a_{j}$ and bj$b_{j}$ such that 
 π=((2n)!!(2n−1)!!)2{nk+a1nk−1+⋯+aknk+1+b1nk+⋯+bk+1+O(1n2k+3)},n→∞,$$ \pi= \biggl(\frac{(2n)!!}{(2n-1)!!} \biggr)^{2} \biggl\{ \frac {n^{k}+a_{1}n^{k-1}+\cdots+a_{k}}{n^{k+1}+b_{1}n^{k}+\cdots+b_{k+1}}+O \biggl(\frac{1}{n^{2k+3}} \biggr) \biggr\} ,\quad n\to\infty, $$ where k≥0$k\geq0$ is any given integer. Based on the obtained result, we establish a more accurate formula for approximating π, which refines some known results.
Refinements of Gurland's formula for pi
The aim of this paper is to refine Gurland's formula for approximating pi. We prove the complete monotonicity of a class of functions related to Gurland's formula, and then we state some sharp inequalities.
Computational Aspects of Linear Control
Introduction. 1. Control of linear systems. 2. Formal orthogonal polynomials. 3. Pade approximations. 4. Transform inversion. 5. Linear algebra issues. 6. Lanczos tridiagonalization process. 7. Systems of linear algebraic equations. 8. Regularization of ill-conditioned systems. 9. Sylvester and riccati equations. 10. Topics on nonlinear differential equations. 11. Appendix: the mathematics of model reduction. Index.