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.
School Principals and Education Law: What do they know, what do they need to know?
Principals now work in complex and challenging environments where uncertainty and change are the hallmarks of their roles and responsibilities. As such, the knowledge and capability demands on principals have expanded, including those related to education law. While these matters attracted some research interest a number of years ago, there has been little recent work in the area of principals and education law. This article reports on an exploratory study into aspects of the legal knowledge held by Tasmanian government school principals, particularly concerning non-sexual physical contact between teachers and students. The research was undertaken using a small-scale, mixed-methods research design, which required principals to respond to various legal scenarios. Three key findings emerged from the study. First, principals used two different levels of working knowledge about education law  one related to legal problems, and the other to legally-related routine activities. Second, on the particular topic of physical contact, some knowledge held by principals was not legally accurate. Third, for major legal issues, participants indicated that they acquired access to information from legal experts. The situation for routine legal matters was less clear, although in-service training and practical experience were identified as potential sources of knowledge. Participants recognised the importance of a sound knowledge of education law, especially for dealing with security and safety issues and preferred to access further information through in-service training. Notably, the findings of the study are broadly consistent with those from earlier Australian and international research, suggesting that much remains to be done in the area of principals’ education law knowledge.