A computer proof of Turán's inequality.
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A proof of a conjecture of Knuth.
Paule, Peter (1996)
Experimental Mathematics
About a new kind of Ramanujan-type series.
Guillera, Jesús (2003)
Experimental Mathematics
Accelerated series for universal constants, by the WZ method.
Wilf, Herbert S. (1999)
Discrete Mathematics and Theoretical Computer Science. DMTCS [electronic only]
An Apéry-like difference equation for Catalan's constant.
Zudilin, W. (2003)
The Electronic Journal of Combinatorics [electronic only]
Analytic and combinatoric aspects of Hurwitz polyzêtas
Jean-Yves Enjalbert, Hoang Ngoc Minh (2007)
Journal de Théorie des Nombres de Bordeaux
In this work, a symbolic encoding of generalized Di-richlet generating series is found thanks to combinatorial techniques of noncommutative rational power series. This enables to explicit periodic generalized Dirichlet generating series – particularly the coloured polyzêtas – as linear combinations of Hurwitz polyzêtas. Moreover, the noncommutative version of the convolution theorem gives easily rise to an integral representation of Hurwitz polyzêtas. This representation enables us to build the...
Apéry's double sum is plain sailing indeed.
Schneider, Carsten (2007)
The Electronic Journal of Combinatorics [electronic only]
Computer-free evaluation of an infinite double sum via Euler sums.
Panholzer, Alois, Prodinger, Helmut (2005)
Séminaire Lotharingien de Combinatoire [electronic only]
Finite Rogers-Ramanujan type identities.
Sills, Andrew V. (2003)
The Electronic Journal of Combinatorics [electronic only]
Generalized reciprocity laws for sums of harmonic numbers.
Kuba, Markus, Prodinger, Helmut, Schneider, Carsten (2008)
Integers
Generating function identities for , via the WZ method.
Hessami Pilehrood, Kh., Hessami Pilehrood, T. (2008)
The Electronic Journal of Combinatorics [electronic only]
Harmonic interpolation based on Radon projections along the sides of regular polygons
Irina Georgieva, Clemens Hofreither, Christoph Koutschan, Veronika Pillwein, Thotsaporn Thanatipanonda (2013)
Open Mathematics
Given information about a harmonic function in two variables, consisting of a finite number of values of its Radon projections, i.e., integrals along some chords of the unit circle, we study the problem of interpolating these data by a harmonic polynomial. With the help of symbolic summation techniques we show that this interpolation problem has a unique solution in the case when the chords form a regular polygon. Numerical experiments for this and more general cases are presented.
Historia de las fórmulas y algoritmos para n.
Jesús Guillera Goyanes (2007)
Gaceta de la Real Sociedad Matemática Española
Human proofs of identities by Osburn and Schneider.
Prodinger, Helmut (2008)
Integers
HYPERG: a Maple package for manipulating hypergeometric series.
Gauthier, Bruno (1999)
Séminaire Lotharingien de Combinatoire [electronic only]
In praise of an elementary identity of Euler.
Bhatnagar, Gaurav (2011)
The Electronic Journal of Combinatorics [electronic only]
Infinite families of accelerated series for some classical constants by the Markov-WZ Method.
Mohammed, Mohamud (2005)
Discrete Mathematics and Theoretical Computer Science. DMTCS [electronic only]
Nested derivatives: a simple method for computing series expansions of inverse functions.
Dominici, Diego (2003)
International Journal of Mathematics and Mathematical Sciences
On the modes of polynomials derived from nondecreasing sequences.
Dou, Donna Q.J., Yang, Arthur L.B. (2011)
The Electronic Journal of Combinatorics [electronic only]
Ratio monotonicity of polynomials derived from nondecreasing sequences.
Chen, William Y.C., Yang, Arthur L.B., Zhou, Elaine L.F. (2010)
The Electronic Journal of Combinatorics [electronic only]
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