Elementary Functions - 4.19 Maclaurin Series and Laurent Series

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
4.19.E7	${\displaystyle{\displaystyle\ln\left(\frac{\sin z}{z}\right)=\sum_{n=1}^{\infty}\frac{(-1)^{n}2^{2n-1}B_{2n}}{n(2n)!}z^{2n}}}$ \ln@{\frac{\sin@@{z}}{z}} = \sum_{n=1}^{\infty}\frac{(-1)^{n}2^{2n-1}\BernoullinumberB{2n}}{n(2n)!}z^{2n}	${\displaystyle{\displaystyle|z|<\pi}}$	ln((sin(z))/(z)) = sum(((- 1)^(n)* (2)^(2*n - 1)* bernoulli(2*n))/(n*factorial(2*n))*(z)^(2*n), n = 1..infinity)	Log[Divide[Sin[z],z]] == Sum[Divide[(- 1)^(n)* (2)^(2*n - 1)* BernoulliB[2*n],n*(2*n)!]*(z)^(2*n), {n, 1, Infinity}, GenerateConditions->None]	Failure	Failure	Successful [Tested: 7]	Successful [Tested: 7]
4.19.E8	${\displaystyle{\displaystyle\ln\left(\cos z\right)=\sum_{n=1}^{\infty}\frac{(-1)^{n}2^{2n-1}(2^{2n}-1)B_{2n}}{n(2n)!}z^{2n}}}$ \ln@{\cos@@{z}} = \sum_{n=1}^{\infty}\frac{(-1)^{n}2^{2n-1}(2^{2n}-1)\BernoullinumberB{2n}}{n(2n)!}z^{2n}	${\displaystyle{\displaystyle|z|<\frac{1}{2}\pi}}$	ln(cos(z)) = sum(((- 1)^(n)* (2)^(2*n - 1)*((2)^(2*n)- 1)*bernoulli(2*n))/(n*factorial(2*n))*(z)^(2*n), n = 1..infinity)	Log[Cos[z]] == Sum[Divide[(- 1)^(n)* (2)^(2*n - 1)*((2)^(2*n)- 1)*BernoulliB[2*n],n*(2*n)!]*(z)^(2*n), {n, 1, Infinity}, GenerateConditions->None]	Failure	Failure	Manual Skip!	Successful [Tested: 6]
4.19.E9	${\displaystyle{\displaystyle\ln\left(\frac{\tan z}{z}\right)=\sum_{n=1}^{\infty}\frac{(-1)^{n-1}2^{2n}(2^{2n-1}-1)B_{2n}}{n(2n)!}z^{2n}}}$ \ln@{\frac{\tan@@{z}}{z}} = \sum_{n=1}^{\infty}\frac{(-1)^{n-1}2^{2n}(2^{2n-1}-1)\BernoullinumberB{2n}}{n(2n)!}z^{2n}	${\displaystyle{\displaystyle|z|<\frac{1}{2}\pi}}$	ln((tan(z))/(z)) = sum(((- 1)^(n - 1)* (2)^(2*n)*((2)^(2*n - 1)- 1)*bernoulli(2*n))/(n*factorial(2*n))*(z)^(2*n), n = 1..infinity)	Log[Divide[Tan[z],z]] == Sum[Divide[(- 1)^(n - 1)* (2)^(2*n)*((2)^(2*n - 1)- 1)*BernoulliB[2*n],n*(2*n)!]*(z)^(2*n), {n, 1, Infinity}, GenerateConditions->None]	Failure	Failure	Manual Skip!	Successful [Tested: 6]