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Keywords
(1)
Formal Power Series
Related Publications
(4)
Power Series in Computer Algebra
Maple v language...
Concrete Mathematics: A Foundation for Computer Science
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Maple package on formal power series
Maple package on formal power series,D. Gruntz,W. Koepf
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Maple package on formal power series
(
Citations: 8
)
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D. Gruntz
,
W. Koepf
Published in 1995.
Cumulative
Annual
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]]);...
...After loading the FPS package [
10
] > with(share): with(FPS):...
...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)...
Wolfram Koepf
.
Computer Algebra Algorithms for Orthogonal Polynomials and Special Fun...
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Citations
(8)
Duplication coefficients via generating functions
(
Citations: 1
)
Hamza Chaggara
,
Wolfram Koepf
Journal:
Complex Variables and Elliptic Equations
, vol. 52, no. 6, pp. 537549, 2007
Power series, Bieberbach conjecture and the de Branges and Weinstein functions
(
Citations: 3
)
Wolfram Koepf
Conference:
International Symposium on Symbolic and Algebraic Computation  ISSAC
, pp. 169175, 2003
Software for the Algorithmic Work with Orthogonal Polynomials and Special Functions
(
Citations: 2
)
Wolfram Koepf
Published in 1998.
The algebra of holonomic equations
(
Citations: 2
)
Wolfram Koepf
Journal:
Mathematische Semesterberichte
, vol. 44, no. 2, pp. 173194, 1997
A package on orthogonal polynomials and special functions
Wolfram Koepf
Published in 1997.