Sentences with POWER-SERIES
Check out our example sentences below to help you understand the context.Sentences
1
"The power series expansion of sin(x) as an infinite sum is: x - (x^3)/3! + (x^5)/5! - (x^7)/7! + ..."
2
"The Maclaurin series is a special case of a power series, where the center of expansion is at x = 0."
3
"A power series can converge either for all values of x or only in a certain interval."
4
"The power series representation of the function e^x is: 1 + x + (x^2)/2! + (x^3)/3! + ..."
5
"To find the radius of convergence of a power series, we can use the ratio test."
6
"The power series for the cosine function is: 1 - (x^2)/2! + (x^4)/4! - (x^6)/6! + ..."
7
"A Taylor series is a type of power series that represents a function as an infinite sum of its derivatives."
8
"Finding the coefficients of a power series often involves calculating derivatives."
9
"The power series of the function f(x) = 1/(1 - x) is: 1 + x + x^2 + x^3 + ..."
10
"For a complex function, the power series may have a region of convergence in the complex plane."
11
"The power series expansion of ln(1 + x) as an infinite sum is: x - (x^2)/2 + (x^3)/3 - (x^4)/4 + ..."
12
"The power series representation of the square root function is: 1 + (x/2) - (x^2)/8 + (x^3)/16 - ..."
13
"The power series for the exponential function is: 1 + x + (x^2)/2! + (x^3)/3! + ..."
14
"The convergence of a power series can be affected by the values of x where it is evaluated."
15
"The power series representation of the function arctan(x) is: x - (x^3)/3 + (x^5)/5 - (x^7)/7 + ..."
1
"A power series is a series of functions."
2
"The power series can be used to approximate functions."
3
"Calculating the coefficients of a power series can be a complex task."
4
"The radius of convergence of a power series can be determined using the ratio test."
5
"The Taylor series expansion is a type of power series representation of a function."
6
"Newton's method relies on power series to approximate the roots of an equation."
7
"The convergence of a power series can be affected by the values of its coefficients."
8
"Mathematicians study the properties and behavior of power series in complex analysis."
9
"The addition and multiplication of power series can be defined using algebraic operations."
