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- https://math.libretexts.org/Courses/Coastline_College/Math_C185%3A_Calculus_II_(Tran)/07%3A_Power_Series/7.02%3A_Power_Series_and_FunctionsA power series is a type of series with terms involving a variable. More specifically, if the variable is x, then all the terms of the series involve powers of x. As a result, a power series can be th...A power series is a type of series with terms involving a variable. More specifically, if the variable is x, then all the terms of the series involve powers of x. As a result, a power series can be thought of as an infinite polynomial. Power series are used to represent common functions and also to define new functions. In this section we define power series and show how to determine when a power series converges and when it diverges. We also show how to represent certain functions using power
- https://math.libretexts.org/Courses/SUNY_Geneseo/Math_222_Calculus_2/05%3A_Power_Series/5.01%3A_Power_Series_and_FunctionsA power series is a type of series with terms involving a variable. More specifically, if the variable is x, then all the terms of the series involve powers of x. As a result, a power series can be th...A power series is a type of series with terms involving a variable. More specifically, if the variable is x, then all the terms of the series involve powers of x. As a result, a power series can be thought of as an infinite polynomial. Power series are used to represent common functions and also to define new functions. In this section we define power series and show how to determine when a power series converges and when it diverges. We also show how to represent certain functions using power
- https://math.libretexts.org/Bookshelves/Calculus/Calculus_(Guichard)/11%3A_Sequences_and_Series/11.09%3A_Power_SeriesThe geometric series has a special feature that makes it unlike a typical polynomial---the coefficients of the powers of xx are the same, namely kk . We will need to allow more general coefficients...The geometric series has a special feature that makes it unlike a typical polynomial---the coefficients of the powers of xx are the same, namely kk . We will need to allow more general coefficients if we are to get anything other than the geometric series.
- https://math.libretexts.org/Under_Construction/Purgatory/Book%3A_Active_Calculus_(Boelkins_et_al.)/08%3A_Sequences_and_Series/8.06%3A_Power_SeriesWe can often assume a solution to a given problem can be written as a power series, then use the information in the problem to determine the coefficients in the power series. This method allows us to ...We can often assume a solution to a given problem can be written as a power series, then use the information in the problem to determine the coefficients in the power series. This method allows us to approximate solutions to certain problems using partial sums of the power series; that is, we can find approximate solutions that are polynomials. The connection between power series and Taylor series is that they are essentially the same thing.
- https://math.libretexts.org/Courses/Al_Akhawayn_University/MTH2301_Multivariable_Calculus/10%3A_Power_Series/10.01%3A_Power_Series_and_FunctionsA power series is a type of series with terms involving a variable. More specifically, if the variable is x, then all the terms of the series involve powers of x. As a result, a power series can be th...A power series is a type of series with terms involving a variable. More specifically, if the variable is x, then all the terms of the series involve powers of x. As a result, a power series can be thought of as an infinite polynomial. Power series are used to represent common functions and also to define new functions. In this section we define power series and show how to determine when a power series converges and when it diverges. We also show how to represent certain functions using power
- https://math.libretexts.org/Courses/Coastline_College/Math_C185%3A_Calculus_II_(Everett)/07%3A_Power_Series/7.02%3A_Power_Series_and_FunctionsA power series is a type of series with terms involving a variable. More specifically, if the variable is x, then all the terms of the series involve powers of x. As a result, a power series can be th...A power series is a type of series with terms involving a variable. More specifically, if the variable is x, then all the terms of the series involve powers of x. As a result, a power series can be thought of as an infinite polynomial. Power series are used to represent common functions and also to define new functions. In this section we define power series and show how to determine when a power series converges and when it diverges. We also show how to represent certain functions using power
- https://math.libretexts.org/Courses/Mission_College/Math_3B%3A_Calculus_2_(Sklar)/10%3A_Power_Series/10.01%3A_Power_Series_and_FunctionsA power series is a type of series with terms involving a variable. More specifically, if the variable is x, then all the terms of the series involve powers of x. As a result, a power series can be th...A power series is a type of series with terms involving a variable. More specifically, if the variable is x, then all the terms of the series involve powers of x. As a result, a power series can be thought of as an infinite polynomial. Power series are used to represent common functions and also to define new functions. In this section we define power series and show how to determine when a power series converges and when it diverges. We also show how to represent certain functions using power
- https://math.libretexts.org/Courses/Cosumnes_River_College/Math_401%3A_Calculus_II_-_Integral_Calculus/04%3A_Power_Series/4.01%3A_Power_Series_and_FunctionsThis section introduces power series, expressing functions as infinite series in terms of powers of x. It covers convergence intervals, techniques to find these intervals, and how to represent fun...This section introduces power series, expressing functions as infinite series in terms of powers of x. It covers convergence intervals, techniques to find these intervals, and how to represent functions using power series. Examples illustrate how to build power series representations for various functions, setting the stage for using series in calculus applications like function approximation and solving differential equations.
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_III%3A_Series_and_Vector_Calculus/02%3A_Power_Series/2.01%3A_Power_Series_and_FunctionsA power series is a type of series with terms involving a variable. More specifically, if the variable is x, then all the terms of the series involve powers of x. As a result, a power series can be th...A power series is a type of series with terms involving a variable. More specifically, if the variable is x, then all the terms of the series involve powers of x. As a result, a power series can be thought of as an infinite polynomial. Power series are used to represent common functions and also to define new functions. In this section we define power series and show how to determine when a power series converges and when it diverges. We also show how to represent certain functions using power
- https://math.libretexts.org/Courses/Community_College_of_Denver/MAT_2420_Calculus_II/06%3A_Power_Series/6.01%3A_Power_Series_and_FunctionsA power series is a type of series with terms involving a variable. More specifically, if the variable is x, then all the terms of the series involve powers of x. As a result, a power series can be th...A power series is a type of series with terms involving a variable. More specifically, if the variable is x, then all the terms of the series involve powers of x. As a result, a power series can be thought of as an infinite polynomial. Power series are used to represent common functions and also to define new functions. In this section we define power series and show how to determine when a power series converges and when it diverges. We also show how to represent certain functions using power
- https://math.libretexts.org/Workbench/MAT_2420_Calculus_II/06%3A_Power_Series/6.02%3A_Power_Series_and_FunctionsA power series is a type of series with terms involving a variable. More specifically, if the variable is x, then all the terms of the series involve powers of x. As a result, a power series can be th...A power series is a type of series with terms involving a variable. More specifically, if the variable is x, then all the terms of the series involve powers of x. As a result, a power series can be thought of as an infinite polynomial. Power series are used to represent common functions and also to define new functions. In this section we define power series and show how to determine when a power series converges and when it diverges. We also show how to represent certain functions using power
