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- https://math.libretexts.org/Courses/East_Tennesee_State_University/Book%3A_Differential_Equations_for_Engineers_(Lebl)_Cintron_Copy/7%3A_Power_series_methods/7.3%3A_Singular_Points_and_the_Method_of_FrobeniusWhile behavior of ODEs at singular points is more complicated, certain singular points are not especially difficult to solve. Let us look at some examples before giving a general method. We may be luc...While behavior of ODEs at singular points is more complicated, certain singular points are not especially difficult to solve. Let us look at some examples before giving a general method. We may be lucky and obtain a power series solution using the method of the previous section, but in general we may have to try other things.
- https://math.libretexts.org/Bookshelves/Differential_Equations/Partial_Differential_Equations_(Walet)/10%3A_Bessel_Functions_and_Two-Dimensional_Problems
- https://math.libretexts.org/Courses/City_College_of_San_Francisco/CCSF_Calculus/17%3A_Second-Order_Differential_Equations/17.05%3A_Series_Solutions_of_Differential_EquationsIn some cases, power series representations of functions and their derivatives can be used to find solutions to differential equations.
- https://math.libretexts.org/Bookshelves/Differential_Equations/Partial_Differential_Equations_(Walet)/10%3A_Bessel_Functions_and_Two-Dimensional_Problems/10.04%3A_Bessel_Functions_of_General_OrderThe recurrence relation for the Bessel function of general order ±ν can now be solved by using the gamma function.
- https://math.libretexts.org/Bookshelves/Calculus/Calculus_(OpenStax)/17%3A_Second-Order_Differential_Equations/17.04%3A_Series_Solutions_of_Differential_EquationsIn some cases, power series representations of functions and their derivatives can be used to find solutions to differential equations.
- https://math.libretexts.org/Courses/Lake_Tahoe_Community_College/MAT-204%3A_Differential_Equations_for_Science_(Lebl_and_Trench)/09%3A_Power_series_methods/9.03%3A_Singular_Points_and_the_Method_of_FrobeniusWhile behavior of ODEs at singular points is more complicated, certain singular points are not especially difficult to solve. Let us look at some examples before giving a general method. We may be luc...While behavior of ODEs at singular points is more complicated, certain singular points are not especially difficult to solve. Let us look at some examples before giving a general method. We may be lucky and obtain a power series solution using the method of the previous section, but in general we may have to try other things.
- https://math.libretexts.org/Bookshelves/Differential_Equations/Differential_Equations_for_Engineers_(Lebl)/7%3A_Power_series_methods/7.3%3A_Singular_Points_and_the_Method_of_FrobeniusWhile behavior of ODEs at singular points is more complicated, certain singular points are not especially difficult to solve. Let us look at some examples before giving a general method. We may be luc...While behavior of ODEs at singular points is more complicated, certain singular points are not especially difficult to solve. Let us look at some examples before giving a general method. We may be lucky and obtain a power series solution using the method of the previous section, but in general we may have to try other things.
- https://math.libretexts.org/Courses/Coastline_College/Math_C285%3A_Linear_Algebra_and_Diffrential_Equations_(Tran)/16%3A_Power_series_methods/16.03%3A_Singular_Points_and_the_Method_of_FrobeniusWhile behavior of ODEs at singular points is more complicated, certain singular points are not especially difficult to solve. Let us look at some examples before giving a general method. We may be luc...While behavior of ODEs at singular points is more complicated, certain singular points are not especially difficult to solve. Let us look at some examples before giving a general method. We may be lucky and obtain a power series solution using the method of the previous section, but in general we may have to try other things.
- https://math.libretexts.org/Bookshelves/Differential_Equations/Introduction_to_Partial_Differential_Equations_(Herman)/05%3A_Non-sinusoidal_Harmonics_and_Special_Functions/5.05%3A_Fourier-Bessel_SeriesBessel functions arise in many problems in physics possessing cylindrical symmetry such as the vibrations of circular drumheads and the radial modes in optical fibers. They also provide us with anothe...Bessel functions arise in many problems in physics possessing cylindrical symmetry such as the vibrations of circular drumheads and the radial modes in optical fibers. They also provide us with another orthogonal set of basis functions.
