Notations

• $\ln x$ — the natural logarithm, also denoted in many sources as $\log x$.
• Direct trigonometric functions are denoted as $\sin x,\,\cos x,\,\tan x,\,\cot x$.
• Inverse trigonometric functions are denoted as $\arcsin x,\,\arccos x,\,\arctan x,\,\operatorname{arccot}x$ (and never as $\tan^{-1}x$, to avoid any confusion with powers).
• Parentheses around the argument is usually omitted if the next term is an integer, named constant, variable, radical, or function name, e.g: $\ln2,\,\ln\pi,\,\ln\sqrt{2\pi},\,\ln\sin x,\,\ln\ln x$.
• Expressions like $\ln2\ln3$ should be understood as $(\ln(2))\cdot(\ln(3))$.
• Expressions like $\ln^53,\,\sin^2x$ should be understood as $(\ln(2))^5,\,(\sin(x))^2$.
• $\zeta(x)$ — the Riemann zeta function.
• $\zeta_3,\,\zeta_5,\,$ etc. — values of $\zeta(x)$ for odd positive integer arguments. Values at even arguments are always expanded in terms of $\pi$.