This is the part for which I obtained the consent of the professor.
Relationship between and	This formula is unnatural from a commonsense standpoint, but this is natural if we look at this carefully. Evaluating no.1 Evaluating no.2 Evaluating no.3
Relationship between and , No.2	The function is bounded variation.
Application to Taylor Series
Periodicity of Function

Full explanation (PDF)
Integral relation	05/2005
Property of laurent expansion	05/2005

Discovery I received
Application to differential geometry	08/2005

In the back of the desk drawer.
Calculate beta funtion	simple computation technique
Explaining = -1	This explanation is like a joke
Relation between me and mathematics	The self-introduction and the inside story