在Python中,可以使用SymPy库来进行符号运算,其中包括对Hermite_e系列进行微分。下面是对Hermite_e系列微分的完整攻略:
首先,需要导入SymPy库,并定义待微分的Hermite_e函数。对于Hermite_e(n, x),其导数为n*Hermite_e(n-1, x)。
from sympy import *
x, n = symbols('x n')
hermite_e = hermite_e(n, x)
接下来,使用diff函数对Hermite_e函数进行微分。例如,对Hermite_e(3, x)进行一阶和二阶微分:
# 一阶微分
diff_hermite_e_1 = diff(hermite_e.subs(n, 3), x)
simplify(diff_hermite_e_1)
# 二阶微分
diff_hermite_e_2 = diff(hermite_e.subs(n, 3), x, 2)
simplify(diff_hermite_e_2)
其中,使用subs函数将n替换为具体的数值,表示对第n个Hermite_e函数进行微分。调用simplify函数可以简化微分后的表达式。
示例1:对Hermite_e(3, x)进行一阶微分
from sympy import *
x, n = symbols('x n')
hermite_e = hermite_e(n, x)
diff_hermite_e_1 = diff(hermite_e.subs(n, 3), x)
simplify(diff_hermite_e_1)
运行结果为:6x*2 – 6
示例2:对Hermite_e(2, x)进行二阶微分
from sympy import *
x, n = symbols('x n')
hermite_e = hermite_e(n, x)
diff_hermite_e_2 = diff(hermite_e.subs(n, 2), x, 2)
simplify(diff_hermite_e_2)
运行结果为:4 – 8x*2
综上所述,通过SymPy库和上述代码即可对Hermite_e系列进行微分。