oo ____ \ ` \ n n + 1 3*n \ (-1) *2 *(x - 1) / --------------------------- / (2*n + 1)*(n + 2)*(3*n + 1) /___, n = 0
Sum((((-1)^n*2^(n + 1))*(x - 1)^(3*n))/((((2*n + 1)*(n + 2))*(3*n + 1))), (n, 0, oo))
// -pi*I / pi*I\ pi*I / 5*pi*I\ / pi*I\ / 3*pi*I\ \ || / ___________ \ ------ | ___________ ----| ---- | ___________ ------| | ___________ ----| | ___________ ------| | || / 3 pi*I\ 2/3 | 3 ___ 3 / 3 pi*I| 2/3 3 | 3 ___ 3 / 3 3 | 2/3 3 | 3 ___ 3 / 3 3 | ___ | ___ / 3 2 | ___ | ___ / 3 2 | | || 1 log\1 - 2*(-1 + x) *e / 3*2 *log\1 - \/ 2 *\/ (-1 + x) *e / 3*2 *e *log\1 - \/ 2 *\/ (-1 + x) *e / 3*2 *e *log\1 - \/ 2 *\/ (-1 + x) *e / I*\/ 2 *log\1 - \/ 2 *\/ (-1 + x) *e / I*\/ 2 *log\1 - \/ 2 *\/ (-1 + x) *e / | 3| | ||------------ - -------------------------- + ------------------------------------------ - -------------------------------------------------- - -------------------------------------------------- - ------------------------------------------- + --------------------------------------------- for 2*|(-1 + x) | <= 1| || 3 6 ___________ ___________ ___________ ___________ ___________ | ||30*(-1 + x) 60*(-1 + x) 3 / 3 3 / 3 3 / 3 / 3 / 3 | || 10*\/ (-1 + x) 10*\/ (-1 + x) 10*\/ (-1 + x) 3*\/ (-1 + x) 3*\/ (-1 + x) | || | 2*|< oo | || ____ | || \ ` | || \ n n 3*n | || \ (-1) *2 *(-1 + x) | || ) ----------------------- otherwise | || / 3 2 | || / 2 + 6*n + 11*n + 17*n | || /___, | \\ n = 0 /
2*Piecewise((1/(30*(-1 + x)^3) - log(1 - 2*(-1 + x)^3*exp_polar(pi*i))/(60*(-1 + x)^6) + 3*2^(2/3)*log(1 - 2^(1/3)*((-1 + x)^3)^(1/3)*exp_polar(pi*i))/(10*((-1 + x)^3)^(1/3)) - 3*2^(2/3)*exp(-pi*i/3)*log(1 - 2^(1/3)*((-1 + x)^3)^(1/3)*exp_polar(pi*i/3))/(10*((-1 + x)^3)^(1/3)) - 3*2^(2/3)*exp(pi*i/3)*log(1 - 2^(1/3)*((-1 + x)^3)^(1/3)*exp_polar(5*pi*i/3))/(10*((-1 + x)^3)^(1/3)) - i*sqrt(2)*log(1 - sqrt(2)*sqrt((-1 + x)^3)*exp_polar(pi*i/2))/(3*sqrt((-1 + x)^3)) + i*sqrt(2)*log(1 - sqrt(2)*sqrt((-1 + x)^3)*exp_polar(3*pi*i/2))/(3*sqrt((-1 + x)^3)), 2*Abs((-1 + x)^3) <= 1), (Sum((-1)^n*2^n*(-1 + x)^(3*n)/(2 + 6*n^3 + 11*n + 17*n^2), (n, 0, oo)), True))
x^n/n
(x-1)^n
1/2^(n!)
n^2/n!
x^n/n!
k!/(n!*(n+k)!)
csc(n)^2/n^3
1/n^2
1/n^4
1/n^6
1/n
(-1)^n
(-1)^(n + 1)/n
(n + 2)*(-1)^(n - 1)
(3*n - 1)/(-5)^n
(-1)^(n - 1)*n/(6*n - 5)
(-1)^(n + 1)/n*x^n
(3*n - 1)/(-5)^n