Padé approximant approach to singular properties of quantum gases: the ideal cases

Yuan-Hong Tian(田远鸿),Wen-Du Li(李文都),Yao Shen(沈尧),Wu-Sheng Dai(戴伍圣)

Figure 5. Comparison of various Padé approximants. The Padé approximants ${\left[3/3\right]}_{{f}_{3/2}}\left(z\right)$, ${\left[4/2\right]}_{{f}_{3/2}}\left(z\right)$, ${\left[2/4\right]}_{{f}_{3/2}}\left(z\right)$, ${\left[1/5\right]}_{{f}_{3/2}}\left(z\right)$, and ${\left[5/1\right]}_{{f}_{3/2}}\left(z\right)$ are constructed from the virial expansion with 6 virial coefficients. The Padé approximants ${\left[2/2\right]}_{{f}_{3/2}}\left(z\right)$, ${\left[1/3\right]}_{{f}_{3/2}}\left(z\right)$, and ${\left[3/1\right]}_{{f}_{3/2}}\left(z\right)$ are constructed from the virial expansion with 4 virial coefficients.