Feynman integrals, hypergeometric functions and nested sums

Bejdakic E. Feynman integrals, hypergeometric functions and nested sums. Bielefeld (Germany): Bielefeld University; 2009.In this thesis, we present analytical expansion results of some single-mass-scale four-loop vacuum integrals in 3 and 4 dimensions. After finding hypergeometric representations with half-integer coefficients, we use algorithms which we implemented in FORM to expand these in terms of nested sums