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- https://math.libretexts.org/Courses/Coastline_College/Math_C185%3A_Calculus_II_(Everett)/07%3A_Power_Series/7.03%3A_Properties_of_Power_SeriesPower series can be combined, differentiated, or integrated to create new power series. This capability is particularly useful for a couple of reasons. First, it allows us to find power series represe...Power series can be combined, differentiated, or integrated to create new power series. This capability is particularly useful for a couple of reasons. First, it allows us to find power series representations for certain elementary functions, by writing those functions in terms of functions with known power series. Second, it allows us to define new functions that cannot be written in terms of elementary functions. This capability is particularly useful for solving differential equations.
- https://math.libretexts.org/Courses/Mission_College/Mission_College_MAT_003B/06%3A_Power_Series/6.03%3A_Properties_of_Power_SeriesPower series can be combined, differentiated, or integrated to create new power series. This capability is particularly useful for a couple of reasons. First, it allows us to find power series represe...Power series can be combined, differentiated, or integrated to create new power series. This capability is particularly useful for a couple of reasons. First, it allows us to find power series representations for certain elementary functions, by writing those functions in terms of functions with known power series. Second, it allows us to define new functions that cannot be written in terms of elementary functions. This capability is particularly useful for solving differential equations.
- https://math.libretexts.org/Bookshelves/Calculus/Calculus_(OpenStax)/10%3A_Power_Series/10.02%3A_Properties_of_Power_SeriesPower series can be combined, differentiated, or integrated to create new power series. This capability is particularly useful for a couple of reasons. First, it allows us to find power series represe...Power series can be combined, differentiated, or integrated to create new power series. This capability is particularly useful for a couple of reasons. First, it allows us to find power series representations for certain elementary functions, by writing those functions in terms of functions with known power series. Second, it allows us to define new functions that cannot be written in terms of elementary functions. This capability is particularly useful for solving differential equations.
- https://math.libretexts.org/Courses/Mission_College/Math_3B%3A_Calculus_2_(Sklar)/10%3A_Power_Series/10.02%3A_Properties_of_Power_SeriesPower series can be combined, differentiated, or integrated to create new power series. This capability is particularly useful for a couple of reasons. First, it allows us to find power series represe...Power series can be combined, differentiated, or integrated to create new power series. This capability is particularly useful for a couple of reasons. First, it allows us to find power series representations for certain elementary functions, by writing those functions in terms of functions with known power series. Second, it allows us to define new functions that cannot be written in terms of elementary functions. This capability is particularly useful for solving differential equations.
- https://math.libretexts.org/Courses/City_College_of_San_Francisco/CCSF_Calculus/09%3A_Power_Series/9.02%3A_Properties_of_Power_SeriesThis section explores properties of power series, including convergence, manipulation, and term-by-term differentiation and integration. It explains radius and interval of convergence and provides exa...This section explores properties of power series, including convergence, manipulation, and term-by-term differentiation and integration. It explains radius and interval of convergence and provides examples to illustrate how these properties allow functions to be expressed and manipulated as series within their intervals of convergence.
- https://math.libretexts.org/Courses/City_College_of_San_Francisco/CCSF_Calculus_II__Integral_Calculus_._Lockman_Spring_2024/05%3A_Power_Series/5.02%3A_Properties_of_Power_SeriesPower series can be combined, differentiated, or integrated to create new power series. This capability is particularly useful for a couple of reasons. First, it allows us to find power series represe...Power series can be combined, differentiated, or integrated to create new power series. This capability is particularly useful for a couple of reasons. First, it allows us to find power series representations for certain elementary functions, by writing those functions in terms of functions with known power series. Second, it allows us to define new functions that cannot be written in terms of elementary functions. This capability is particularly useful for solving differential equations.
- https://math.libretexts.org/Courses/Cosumnes_River_College/Math_401%3A_Calculus_II_-_Integral_Calculus/04%3A_Power_Series/4.02%3A_Properties_of_Power_SeriesThis section explores properties of power series, including convergence, manipulation, and term-by-term differentiation and integration. It explains radius and interval of convergence and provides exa...This section explores properties of power series, including convergence, manipulation, and term-by-term differentiation and integration. It explains radius and interval of convergence and provides examples to illustrate how these properties allow functions to be expressed and manipulated as series within their intervals of convergence.
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_III%3A_Series_and_Vector_Calculus/02%3A_Power_Series/2.02%3A_Properties_of_Power_SeriesPower series can be combined, differentiated, or integrated to create new power series. This capability is particularly useful for a couple of reasons. First, it allows us to find power series represe...Power series can be combined, differentiated, or integrated to create new power series. This capability is particularly useful for a couple of reasons. First, it allows us to find power series representations for certain elementary functions, by writing those functions in terms of functions with known power series. Second, it allows us to define new functions that cannot be written in terms of elementary functions. This capability is particularly useful for solving differential equations.
- https://math.libretexts.org/Courses/Coastline_College/Math_C185%3A_Calculus_II_(Tran)/07%3A_Power_Series/7.03%3A_Properties_of_Power_SeriesPower series can be combined, differentiated, or integrated to create new power series. This capability is particularly useful for a couple of reasons. First, it allows us to find power series represe...Power series can be combined, differentiated, or integrated to create new power series. This capability is particularly useful for a couple of reasons. First, it allows us to find power series representations for certain elementary functions, by writing those functions in terms of functions with known power series. Second, it allows us to define new functions that cannot be written in terms of elementary functions. This capability is particularly useful for solving differential equations.
- https://math.libretexts.org/Courses/Lake_Tahoe_Community_College/Interactive_Calculus_Q3/02%3A_Power_Series/2.03%3A_Properties_of_Power_SeriesPower series can be combined, differentiated, or integrated to create new power series. This capability is particularly useful for a couple of reasons. First, it allows us to find power series represe...Power series can be combined, differentiated, or integrated to create new power series. This capability is particularly useful for a couple of reasons. First, it allows us to find power series representations for certain elementary functions, by writing those functions in terms of functions with known power series. Second, it allows us to define new functions that cannot be written in terms of elementary functions. This capability is particularly useful for solving differential equations.
- https://math.libretexts.org/Courses/Mission_College/Math_3B%3A_Calculus_II_(Reed)/10%3A_Power_Series/10.02%3A_Properties_of_Power_SeriesPower series can be combined, differentiated, or integrated to create new power series. This capability is particularly useful for a couple of reasons. First, it allows us to find power series represe...Power series can be combined, differentiated, or integrated to create new power series. This capability is particularly useful for a couple of reasons. First, it allows us to find power series representations for certain elementary functions, by writing those functions in terms of functions with known power series. Second, it allows us to define new functions that cannot be written in terms of elementary functions. This capability is particularly useful for solving differential equations.
