A Difference Ring Theory for Symbolic Summation

Understand

A summation framework is developed that enhances Karr's difference field approach.

• It covers not only indefinite nested sums and products in terms of transcendental extensions, but it can treat, e.g., nested products defined over roots of unity.
• The theory of the so-called $R\Pi\Sigma^*$-extensions is supplemented by algorithms that support the construction of such difference rings automatically and that assist in the task to tackle symbolic summation problems.
• Algorithms are presented that solve parameterized telescoping equations, and more generally parameterized first-order difference equations, in the given difference ring.