def taylor_term(n, x, *previous_terms):
if n < 0:
return S.Zero
else:
x = sympify(x)
if len(previous_terms) > 1:
p = previous_terms[-1]
return ((3**(S(1)/3)*x)**(-n)*(3**(S(1)/3)*x)**(n + 1)*sin(pi*(2*n/3 + S(4)/3))*C.factorial(n) *
gamma(n/3 + S(2)/3)/(sin(pi*(2*n/3 + S(2)/3))*C.factorial(n + 1)*gamma(n/3 + S(1)/3)) * p)
else:
return (S.One/(3**(S(2)/3)*pi) * gamma((n+S.One)/S(3)) * sin(2*pi*(n+S.One)/S(3)) /
C.factorial(n) * (root(3, 3)*x)**n)
def taylor_term(n, x, *previous_terms):
if n < 0:
return S.Zero
else:
x = sympify(x)
if len(previous_terms) > 1:
p = previous_terms[-1]
return ((3**(S(1)/3)*x)**(-n)*(3**(S(1)/3)*x)**(n + 1)*sin(pi*(2*n/3 + S(4)/3))*C.factorial(n) *
gamma(n/3 + S(2)/3)/(sin(pi*(2*n/3 + S(2)/3))*C.factorial(n + 1)*gamma(n/3 + S(1)/3)) * p)
else:
return (S.One/(3**(S(2)/3)*pi) * gamma((n+S.One)/S(3)) * sin(2*pi*(n+S.One)/S(3)) /
C.factorial(n) * (root(3, 3)*x)**n)
def taylor_term(n, x, *previous_terms):
if n < 0:
return S.Zero
else:
x = sympify(x)
if len(previous_terms) > 1:
p = previous_terms[-1]
return (3**(S(1)/3)*x * Abs(sin(2*pi*(n + S.One)/S(3))) * C.factorial((n - S.One)/S(3)) /
((n + S.One) * Abs(cos(2*pi*(n + S.Half)/S(3))) * C.factorial((n - 2)/S(3))) * p)
else:
return (S.One/(root(3, 6)*pi) * gamma((n + S.One)/S(3)) * Abs(sin(2*pi*(n + S.One)/S(3))) /
C.factorial(n) * (root(3, 3)*x)**n)
def taylor_term(n, x, *previous_terms):
if n < 0:
return S.Zero
else:
x = sympify(x)
if len(previous_terms) > 1:
p = previous_terms[-1]
return (3**(S(1)/3)*x * Abs(sin(2*pi*(n + S.One)/S(3))) * C.factorial((n - S.One)/S(3)) /
((n + S.One) * Abs(cos(2*pi*(n + S.Half)/S(3))) * C.factorial((n - 2)/S(3))) * p)
else:
return (S.One/(root(3, 6)*pi) * gamma((n + S.One)/S(3)) * Abs(sin(2*pi*(n + S.One)/S(3))) /
C.factorial(n) * (root(3, 3)*x)**n)