SymPy学习之Concrete Mathematics

Sum

>>> from sympy.abc import i, k, m, n, x>>> from sympy import Sum, factorial, oo, IndexedBase, Function>>> Sum(k, (k, 1, m))Sum(k, (k, 1, m))>>> Sum(k, (k, 1, m)).doit()m**2/2 + m/2>>> Sum(k**2, (k, 1, m))Sum(k**2, (k, 1, m))>>> Sum(k**2, (k, 1, m)).doit()m**3/3 + m**2/2 + m/6>>> Sum(x**k, (k, 0, oo))Sum(x**k, (k, 0, oo))>>> Sum(x**k, (k, 0, oo)).doit()Piecewise((1/(-x + 1), Abs(x) < 1), (Sum(x**k, (k, 0, oo)), True))>>> Sum(x**k/factorial(k), (k, 0, oo)).doit()exp(x)

Product

>>> from sympy.abc import a, b, i, k, m, n, x>>> from sympy import Product, factorial, oo>>> Product(k, (k, 1, m))Product(k, (k, 1, m))>>> Product(k, (k, 1, m)).doit()factorial(m)>>> Product(k**2,(k, 1, m))Product(k**2, (k, 1, m))>>> Product(k**2,(k, 1, m)).doit()factorial(m)**2