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Maple package on formal power series

# Maple package on formal power series,D. Gruntz,W. Koepf

Maple package on formal power series
Published in 1995.

## Citation Context (6)

• ...for F(t) and convert this differential equation into the above holonomic recurrence equation for the corresponding series coefficients by the Maple FPS package (see [12] and [14])...

### Hamza Chaggara, et al. Duplication coefficients via generating functions

• ...If the result is simple enough, the FPS (formal power series) procedure of the Maple package FPS.mpl ([7], [5], [6]) computes this series, even if it is a Laurent series (including negative powers) or Puiseux series (including rational powers)...

### Wolfram Koepf. Power series, Bieberbach conjecture and the de Branges and Weinstein f...

• ...> det([[1,2*a,3],[5,6,7],[9,10,11]]); 16 + 16a and the eigenvalues and eigenvectors for a = 1: > eigenvalues([[1,2,3],[5,6,7],[9,10,11]]); 0, 9 + p 105, 9 p 105...
• ...> det([[1,2*a,3],[5,6,7],[9,10,11]]); 16 + 16a and the eigenvalues and eigenvectors for a = 1: > eigenvalues([[1,2,3],[5,6,7],[9,10,11]]); 0, 9 + p 105, 9 p 105...
• ...> eigenvectors([[1,2,3],[5,6,7],[9,10,11]]);...
• ...The algorithm behind this procedure is the following ([14], [10]):...

### Wolfram Koepf. Software for the Algorithmic Work with Orthogonal Polynomials and Spec...

• ...This differential equation can be found using a method given in [20]–[21], whereas the sum algorithm generates the second order differential equation...
• ...This result can also be obtained by the method given in [20]–[21]...

### Wolfram Koepf. The algebra of holonomic equations

• ...Let us remark that as a general reference we use the book [11], the computer algebra system Maple [16], [4] and the Maple packages FPS [9], [7], gfun [19], hsum [11], infhsum [22], hsols [21], qsum [2] and retode [13]...
• ...hence ak = 1 k! . If the result is simple enough, the FPS (formal power series) procedure of the Maple package FPS.mpl ([9], [7]) computes this series, even if it is a Laurent series (including negative powers) or Puiseux series (including rational powers)...

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## Citations (8)

### Duplication coefficients via generating functions(Citations: 1)

Journal: Complex Variables and Elliptic Equations , vol. 52, no. 6, pp. 537-549, 2007

### Software for the Algorithmic Work with Orthogonal Polynomials and Special Functions(Citations: 2)

Published in 1998.

### The algebra of holonomic equations(Citations: 2)

Journal: Mathematische Semesterberichte , vol. 44, no. 2, pp. 173-194, 1997

### A package on orthogonal polynomials and special functions

Published in 1997.