There are specifically 2 areas I shall be focussing on in my self learning journey of mathematics. They are:-
1. Elliptic functions - Elliptic functions are damn important. Jacobi, Abel, Weirstrass, Gauss views and theories are crucial.
2. Pochhammer symbol and acceleration and deceleration - This is my idea. And I wish to study the shift in Pochhammer symbol due to squares and square roots.
Complex functions are important. And I wish to learn this topic too.
1. Elliptic functions - Elliptic functions are damn important. Jacobi, Abel, Weirstrass, Gauss views and theories are crucial.
2. Pochhammer symbol and acceleration and deceleration - This is my idea. And I wish to study the shift in Pochhammer symbol due to squares and square roots.
Complex functions are important. And I wish to learn this topic too.
14 comments:
I think there is q-Pochhammer symbol. So there is no point in learning the second point.
I would like to defend my point of circular functions.
If you take dy/dx definition; it is limit of delta y by delta x where delta x tends towards zero. Tends towards zero is focussing on one thing.
Hence circular function.
To me complex conjugate is the ultimate truth. Not right triangle.
Another point is I believe the area of a simple and hence perfect right triangle is zero.
Most importantly, there is no 2 or more in my thoughts.
I will align with only those who believe in and are 100% for Taylor series. Not more. Not less.
I cry for myself. For I shall have to dig a grave for myself.
I am so strong in root(n) sorts, that I am afraid of myself. Three important Gauss things namely "Constructibility of polygon", "Gauss Error Function" and "Gauss constant" are demonstrated with root(n) thinking.
O Lord in heaven let me not dig my own grave !!
Most of us are salary earners. I wonder about decimal point treatement then.
One certain thing is in the calculus of dy/dx which is limit delta y by delta x where delta x tends to zero, is we omit delta x squared. How? 10/3 in salary how?
See. Constructibility is a different issue. You do not need 3.3333. . . . . . to divide a line into three. Just a perpendicular bisector and parallel lines can divide into 3.
And Gauss error functions has error. It is concerned with shape of the curve.
Gauss constant result of mine is meant to be approximate.
The point I wish to make is where is the problem in above?
Basically calculus freaks have to explain omission of delta x squared and higher terms.
And salary earners have to explain 10/3.
Well. I got your point.
root(2) - 3/4(root(3) - root(2)) is constructible. For pentagon.
But is only approximate till 3 places of decimal.
I think I can win this point. 78.6% in my favor.
Sigma series is quite natural in me.
When sigma series is represented in terms of geometric series; then it may not be differentiable or integratable.
However when sigma series is represented in terms of Taylor series, then it is.
Parseval theorem is critical to my knowledge improvement.
I believe in Parseval. And hence am clear in Parseval theorem.
The sigma-integration equivalence is important for me.
When one wishes to differentiate x^x; then he puts f(x) = x^x.
Now this f(x) is no small thing and the meaning is implied that it obeys the Taylor series. This point is important.
Newton then said that Limit f(x+h)/x where h tends to zero. And he allowed for omission of terms of h and higher terms of h.
This finishes.
I am quite clear, upto 100 % in the following:-
1. Beta function
2. Gamma function
3. Parseval theorem
Recollect my illustrated work on
1. Constant e
2. Fourier Series.
Well I can illustrate and explain now 3+2 of above.
I think self learning "Complex Functions" is what is essential. Not elliptic functions.
I have two books. "Complex Analysis" by Purna Chandra Biswal. And "Theory of Complex functions" by Reinhold Remmert.
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