Taylor series expansion

Calculation of a function (f) Taylor series of order n at x0.

single letter
To multiply: write a*b not ab
max 20


This tool calculates the Taylor series expansion of a function.
The usual functions are accepted: sine, cosine, tangent, logarithm (log), exponential, square root, etc. (See table below).

For x0, you can enter numbers (4, 0.2), fractions (3/4) or constants (pi, e).

How to use this calculator ?

Variables A function can have one or more variables, but only one main variable.
A variable is a single lowercase or uppercase letter.
Examples:
A function f with one main variable : f(x) = 4*x
A function g with one main variable x and a secondary parameter m,
g(x) = 4*x*m + x + 1,
In this case, enter x in the “main variable” field
Numbers Use a dot as decimal separator
Operators + (addition),
- (substration),
* (multiplication),
/ (division),
^ (power),
For multiply operator, enter a*b not a.b nor ab. Example: 2*x.
Constants You may use these constants :
pi (approx. 3.14),
e (approx. 2,72)
Examples: f(x) = pi * x or f(x) = e * (x+1+2*e)2
Common Functions You may use theses functions in the expression of f(x)
sqrt(x) (square root),
exp(x) (exponential function),
log(x) or ln (natural logarithm),
Trigonometric functions You may use theses functions in the expression of f(x)
sin (sine),
cos (cosine),
tan (tangent),
cot (cotangent),
sec (secant),
csc (cosecant),
Inverse trigonometric functions You may use theses functions in the expression of f(x)
arcsin (arcsine),
arccos (arccosine),
arctan (arctangent),
arccot (arcotangent),
arcsec (arcsecant),
arccsc (arccosecant),
Hyperbolic Functions You may use theses functions in the expression of f(x)
sinh (hyperbolic sine),
cosh (hyperbolic cosine),
tanh (hyperbolic tangent),
coth (hyperbolic cotangent),
sech (hyperbolic secante),
csch (hyperbolic cosecant)
Inverse hyperbolic functions You may use theses functions in the expression of f(x)
asinh (inverse hyperbolic sine),
acosh (inverse hyperbolic cosine),
atanh (inverse hyperbolic tangent),
acoth (inverse hyperbolic cotangent),
asech (inverse hyperbolic secant),
acsch (inverse hyperbolic cosecant)

See also

Derivative of a function
Primitive calculator
Function limit
Value of a function
Definite Integral