Coverage for /usr/lib/python3/dist-packages/sympy/series/series.py: 50%

1from sympy.core.sympify import sympify 

2 

3 

4def series(expr, x=None, x0=0, n=6, dir="+"): 

5 """Series expansion of expr around point `x = x0`. 

6 

7 Parameters 

8 ========== 

9 

10 expr : Expression 

11 The expression whose series is to be expanded. 

12 

13 x : Symbol 

14 It is the variable of the expression to be calculated. 

15 

16 x0 : Value 

17 The value around which ``x`` is calculated. Can be any value 

18 from ``-oo`` to ``oo``. 

19 

20 n : Value 

21 The number of terms upto which the series is to be expanded. 

22 

23 dir : String, optional 

24 The series-expansion can be bi-directional. If ``dir="+"``, 

25 then (x->x0+). If ``dir="-", then (x->x0-). For infinite 

26 ``x0`` (``oo`` or ``-oo``), the ``dir`` argument is determined 

27 from the direction of the infinity (i.e., ``dir="-"`` for 

28 ``oo``). 

29 

30 Examples 

31 ======== 

32 

33 >>> from sympy import series, tan, oo 

34 >>> from sympy.abc import x 

35 >>> f = tan(x) 

36 >>> series(f, x, 2, 6, "+") 

37 tan(2) + (1 + tan(2)**2)*(x - 2) + (x - 2)**2*(tan(2)**3 + tan(2)) + 

38 (x - 2)**3*(1/3 + 4*tan(2)**2/3 + tan(2)**4) + (x - 2)**4*(tan(2)**5 + 

39 5*tan(2)**3/3 + 2*tan(2)/3) + (x - 2)**5*(2/15 + 17*tan(2)**2/15 + 

40 2*tan(2)**4 + tan(2)**6) + O((x - 2)**6, (x, 2)) 

41 

42 >>> series(f, x, 2, 3, "-") 

43 tan(2) + (2 - x)*(-tan(2)**2 - 1) + (2 - x)**2*(tan(2)**3 + tan(2)) 

44 + O((x - 2)**3, (x, 2)) 

45 

46 >>> series(f, x, 2, oo, "+") 

47 Traceback (most recent call last): 

48 ... 

49 TypeError: 'Infinity' object cannot be interpreted as an integer 

50 

51 Returns 

52 ======= 

53 

54 Expr 

55 Series expansion of the expression about x0 

56 

57 See Also 

58 ======== 

59 

60 sympy.core.expr.Expr.series: See the docstring of Expr.series() for complete details of this wrapper. 

61 """ 

62 expr = sympify(expr) 

63 return expr.series(x, x0, n, dir)