**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 expansion02/2011
Addition, subtraction, multiplication,

and division of algebraic equations
04/2012

**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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