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
Application of Integral Relation
Relation between the regular and principal parts of the Laurent expansion	Its extreme simplicity suggests that it is quite possible that the proof had already been known

Full explanation (PDF)
Integral formulas	Autumn 1975
The series expansion of B-function	Autumn 1977
Integral relation	05/1998
Property of laurent expansion	08/1999 06/2004
n-th integral function	01/2009
Relation between the regular and principal parts of the Laurent expansion	02/2011
Addition, subtraction, multiplication, and division of algebraic equations	04/2012
Definition of the Definite Integral	03/2022

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

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