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CALCOLO DI TERMINI E SERI (CON SAGE):

sage: z = var('z')
sage: hypergeometric([], [], z).series(z, 0)
Order(1)
sage: hypergeometric([], [], z).series(z, 1)
1 + Order(z)
sage: hypergeometric([], [], z).series(z, 2)
1 + 1*z + Order(z^2)
sage: hypergeometric([], [], z).series(z, 3)
1 + 1*z + 1/2*z^2 + Order(z^3)

sage: hypergeometric([-2], [], z).series(z, 3)
1 + (-2)*z + 1*z^2
sage: hypergeometric([-2], [], z).series(z, 6)
1 + (-2)*z + 1*z^2
sage: hypergeometric([-2], [], z).series(z, 6).is_terminating_series()
True
sage: hypergeometric([-2], [], z).series(z, 2)
1 + (-2)*z + Order(z^2)
sage: hypergeometric([-2], [], z).series(z, 2).is_terminating_series()
False

sage: hypergeometric([1], [], z).series(z, 6)
1 + 1*z + 1*z^2 + 1*z^3 + 1*z^4 + 1*z^5 + Order(z^6)
sage: hypergeometric([], [1/2], -z^2/4).series(z, 11)
1 + (-1/2)*z^2 + 1/24*z^4 + (-1/720)*z^6 + 1/40320*z^8 +...
(-1/3628800)*z^10 + Order(z^11)

sage: hypergeometric([1], [5], x).series(x, 5)
1 + 1/5*x + 1/30*x^2 + 1/210*x^3 + 1/1680*x^4 + Order(x^5)

sage: sum(hypergeometric([1, 2], [3], 1/3).terms(6)).n()
1.29788359788360
sage: hypergeometric([1, 2], [3], 1/3).n()
1.29837194594696
sage: hypergeometric([], [], x).series(x, 20)(x=1).n() == e.n()
True