Algorithmic Approach for Formal Fourier Series

Benoit, A.: Algorithmique semi-numerique rapide des series de Tchebychev. Ph.D. Dissertation, cole polytechnique & INRIA, France (2012)

Bronstein I., Semendjajew K., Musiol G., Mühlig H.: Taschenbuch der Mathematik. Harri Deutsch, Frankfurt (2008)

Churchill, R., Brown, J.: Fourier Series and Boundary Value Problems, 3rd edn. McGraw-Hill, Maidenherd (1978)

Cluzeau T., van Hoeij M.: Computing hypergeometric solutions of linear recurrence equations. Appl. Algebra Eng. Commun. Comput. 17(2), 83–115 (2006)

Denkewitz, L.: Fourieranalyse mit Mathematica. Diploma Thesis, HTWK Leipzig, Leipzig (2000). http://www.mathematik.uni-kassel.de/~koepf/Diplome

Dirichlet P.: Sur la convergence des series trigonométriques qui servent à représenter une fonction arbitraire entre des limites données. J. Reine Angew. Math. 4(6), 157169 (1829)

van Hoeij M.: Factorization of differential operators with rational functions coefficients. J. Symb. Comput. 24, 537–561 (1997)

van Hoeij M.: Finite singularities and hypergeometric solutions of linear recurrence equations. J. Pure Appl. Algebra 139, 109–131 (1998)

Horn, P.: Faktorisierung in Schief-Polynomringen. Ph.D. Dissertation. University of Kassel, Kassel (2008). http://kobra.bibliothek.uni-kassel.de/handle/urn:nbn:de:hebis:34-200903022651 .

Koepf W.: Power series in computer algebra. J. Symb. Comput. 13(6), 581–603 (1992)

Koepf W.: Computeralgebra. In: Eine Algorithmisch Orientierte Einführung. Springer, Berlin (2006)

Koepf W.: Hypergeometric summation. An algorithmic approach to summation and special function identities. In: Springer Universitext Series, 2nd edn. Springer, London (2014)

Lewanowicz S., Godoy E., Area I., Ronveaux A., Zarzo A.: Recurrence relations for the coefficients of the Fourier series expansions with respect to q-classical orthogonal polynomials. Numer. Algorithms 23, 3150 (2000)

Monagan, M.B., Geddes, K.O., Heal, K.M., Labahn, G., Vorkoetter, S.M., McCarron, J., DeMarco, P.: Maple Advanced Programming Guide. Maplesoft, Waterloo (2008)

Le Grand Nana Chiadjeu, E.: Algorithmic Computation of Formal Fourier Series. Ph.D. Disseration. University of Kassel, Kassel (2010). http://kobra.bibliothek.uni-kassel.de/handle/urn:nbn:de:hebis:34-2010021132007

Petkovšek M.: Hypergeometric solutions of linear recurrences with polynomial coefficients. J. Symb. Comput. 14, 243–264 (1992)

Petkovšek, M., Wilf, H.S., Zeilberger, D.: A=B. AK Peters, Ltd., Wellesley (1996)

Salvy B., Zimmermann P.: Gfun: a Maple package for the manipulation of generating and holonomic functions in one variable. ACM Trans. Math. Softw. 20.2, 163–177 (1994)

Stanley R.: Differentiably finite power series. Eur. J. Comb. 1, 175–188 (1980)

Stöcker H.: Taschenbuch Mathematischer Formeln und Moderner Verfahren. Harri Deutsch, Frankfurt (1999)

Stuart R.D.: An introduction to Fourier analysis. In: Methuen’s Monographs on Physical Subjects. Methuen & Co. Ltd., London (1961)

Werner, W.: Mathematik lernen mit Maple, vol. 2. Dpunkt, Heidelberg (1998)

Wolfram S.: The Mathematica Book. Wolfram Media und Cambridge University Press, Cambridge (1999)