The following TI-Nspire CAS libraries are licensed under the Gnu Public License v3.0.

Differential Equation Series Library - functions for series solutions of first- and second-order differential equations
Differential Equation Special Functions Library - Bessel Functions, Legendre Functions, Gamma Function, Log-Gamma Function
Fast Fourier Transform Library - functions for Fast Fourier Transform and Inverse Fast Fourier Transform
Fourier Series Library - functions for Fourier, Fourier sine, Fourier cosine series
List Utility Library - utility functions for list manipulations
Simplex Method Library - implementation of the Simplex Method for Linear Programming

To use the libraries:

2. Save the library in the TI-Nspire mylib folder,
3. In the user interface, open the Library pane and select Refresh Libraries

Libraries

deserieslib, v1.01 - functions for series solutions of differential equations:

 Function Name Description de_series_op() Computes the series solutions for a differential equation centered on an ordinary point. de_series_sp() Computes the series solutions for a differential equation centered on a singular point. de_singular_pts() Finds the singular points (if any) of a differential equation. de_indicial_eqn() Calculates the indicial equation and its roots r1 and r2 of a differential equation and a singular point. bessel1() Generates a series for a Bessel function of first order, Jn(x), where n is an integer. help() Displays detailed information about using the library and its functions.

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despecfunc, v1.10 - special functions for solving differential equations:

 Function Name Description besseljn() Returns Jn(x), the value of the Bessel Function of the first kind of integer order n. besselyn() Returns Yn(x), the value of the Bessel Function of the second kind of integer order n. besselvalues() Returns a list containing values of either Jn(x) or Yn(x) and the first and second derivatives of the function. gamma() Returns the value of the Gamma function. help() Displays detailed information about using the library and its functions. legendrepn() Returns an expression for Pn(x), the Legendre polynomial of order n. legendreqn() Returns an expression for Qn(x), the Legendre function of the second kind of order n. lngamma() Returns the value of the natural logarithm of the Gamma function.

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fftlib, v1.00 - functions for Fast Fourier Transform and Inverse Fast Fourier Transform.

 Function Name Description fft() Transform point y values using the Fast Fourier Transform. ifft() Invert transformed point y values using the Inverse Fast Fourier Transform. displayclist() Display a list of values formatted as (real,imaginery) pairs. padlist() Zero-pad a list of point y values to conform to fft() length requirement. unpadlist() Remove zero-padding from a list of values after executing ifft(). help() Displays detailed information about using the library and its functions.

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fourierlib, v1.00 - functions for generating fourier series, fourier cosine series, and fourier sine series.

 Function Name Description fourier() calculate a fourier series to approximate a function over an interval. fouriercos() calculate a fourier cosine series to approximate a function over an interval. fouriersin() calculate a fourier sine series to approximate a function over an interval. fouriercoscoef() return a specified fourier cosine series coefficient for a function. fouriersincoef() return a specified fourier sine series coefficient for a function. help() Displays detailed information about using the library and its functions. isevenfunc() Returns true if a named function is an even function and false if not. isoddfunc() Returns true if a named function is an odd function and false if not.

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listutils, v1.00 - utility functions for manipulating TI-Nspire lists:

 Function Name Description append() Adds an element to the end of a list. insert() Inserts an element into a list after an element at a specified position (index). qsort() sorts a list in ascending order. remove() removes an element at the specified position (index) from the list. reverse() reverses the order of elements in a list.