Analysis and Algebraic Structures of q-Analysis and its Generalizations

• Main Author: Karlsson, Olle
• Format: Others
• Language: English
• Published: Mälardalens högskola, Akademin för utbildning, kultur och kommunikation 2020
• Subjects: calculus; Mathematics; Matematik
• Online Access: http://urn.kb.se/resolve?urn=urn:nbn:se:mdh:diva-48847

In this thesis we explore the concept of q-calculus and its generalisation. We begin by defining q-combinatorics which uses a real number to define a new set of numbers and then use these numbers to get classic combinatoric elements. These results have use when we work on our algebra that are related with this specific real number. We then work out some results involving one of the operators in the algebra. This operator together with a similar operator produces some special differential equations that we explore. Then we go on to define integrals as the inverse operator to the one used for our differential equations. In the last chapter we try to generalise everything we have explored until then.