Does it encompass all?

Did Gauss saw it all? His advocacy of Complex functions.  Basically functions having complex arguments. 

I have the above book. But I feel one needs to understand German language to get into the groove and understand the nuances. Indian English will not be enough to get into the book. Because Riemann is very particular.  Very methodical. Very demanding. Very specific.  In the book.

Abel disagreed. And said that Quintic equations cannot be solved. The world says Abel is correct. Gauss rejected his work. 

I don't know how numbers are treated in far east. In Israel. In America. Forget Europe. 

Hume kya lena hai duniya waalon se? Roti milthi rahe. Bas itna sa khaab hai.

 Good bye. Have a nice day!!

Plus and Minus

 My expressions

Have a nice day !!

Being human

Being human is being oneself.  Myself.  Shiva is above us. Jesus is around us. But being myself is the way and the way the world understands. 

The number m, the e formula,  the cos and sine. The way I see them.

Have a nice day!!

These four screenshots

 I present the following four screenshots.

Hope you like them.

And these too.

Hope you like these too.

Also I would like to remind you of the following two formulas

The expressions above are great for finding the difference in differential of cos(x) and for finding the definite integral for a range of sin(x).

Have a nice day !!

A few lessons to me

Consider the following expressions 

I have used i, the complex number in both. 

One gives a simple cos(x) expressions.  While the other cosh(x). This is a discovery. 

Another point is, now I think I am in a position to get sigma integral equivalence for trigonometric and hyperbolic functions. 

Have a nice day!!

These expressions too on 26th November 2023

These expressions are hereby presented on 27th November 2023. 

Have a nice day  !!

This expression on 26th November 2023

Special thanks to Wolfram alpha.  

I present this expression today. Like many of the earlier expressions this expression too is on e.

Have a nice day !!

I finally got cosine and sine expressions

 I have finally got cosine and sine expressions. Here are they

Have a nice day !!

An engineer son of Allahabad Ganga valley farmer?

An engineer son of Allahabad Ganga valley farmer? Or an engineer son of Kumbakonam Cauvery delta farmer?

The mother of the would be bride needs to decide.

The father in me has decided.  Engineer son of Kumbakonam Cauvery delta farmer. The reason is focus. The Chola name.

Without focus you don't get to understand time. Without time you don't understand constants. Neither XML nor Apps.

I put forward to Google social mindset to decide. Who is more eligible bridegroom?

The story of e

The king had two sons. One of them was interested in the empire. The other was not. The son who was interested in the empire had two sons. One of these was interested in the kingdom the other was not. And so on the kingdom flourished.

1

1  0

1   0    0

1   0    0     0

1   0    0     0     0

. . . . . . . . . 

. . . . . . . . . 

The treasure cleaner had two sons. One of them was interested in the treasure. The other was not. The son who was interested in the treasure had two sons. One of these was interested in the treasure the other was not. And so on the treasure was safeguarded.

2

2  0

2   0    0

2   0    0     0

2   0    0     0     0

. . . . . . . . . 

. . . . . . . . . 

The brahmin of knowledge had two sons. One of them was interested in the knowledge. The other was not. The son who was interested in the knowledge had two sons. One of these was interested in the knowledge the other was not. And so on the knowledge was kept.

3

3  0

3   0    0

3   0    0     0

3   0    0     0     0

. . . . . . . . . 

. . . . . . . . . 

The song of the king is still sung because of the treasure cleaners chain and the brahman knowledge chain. The area the king has influence is the area maintained by the awe of the treasure and the hymns of the brahmans.

More of what I wish to say

 

I wish to state that I am able to show integral and sigma equivalence.  To the best of my knowledge only Parseval was able to demonstrate integral and sigma equivalence.

Have a nice day !!

What I wish to say

 

Have a nice day !!

A general form of my hypergeometric function

Hypergeometric distribution is distribution above binomial distribution. 

When we made a mark | when one bullock went inside cowshed; and || when the second bullock went inside the cowshed and so on we were ignorant and simple. Later we came up with 1,2,3 etc. The problem is we used 1,2,3 not just for the bullock getting inside cowshed but also for the tiger cubs getting inside the den. Is a bullock the same as a tiger cub? No. That is the problem. 

Hypergeometric distribution is not like that.

Here is a general form of the Hypergeometric functions that I did.

You may notice that the results are same if we start from 0 or start from 1.  This is exactly what I was preaching about.  Indians in general give a lot of importance to zero. Shoonyata.  Many feel they are shoonya and do the job of 1 or any numbers till infinity.  They are controlling their egos perhaps. 

Many people think I am Tamil, non hindi and perhaps non US. No sirs. I am a global devotee of Shiva. Of Mohammed. 

Have a nice day !! My best wishes to you!!

Final hypergeometric function

 

Have a nice day !!

My transformed hypergeometric expression now fetching classical result

My transformed hypergeometric functions are fetching classical result. 

It fetches results on e.

Have a nice day !!

Some approximately theorems

I believe I can make upto 4 theorems.  Using calculator and Wolfram alpha. 

Almost a number theorems.  This can be developed and will further reiterate the fact that actually there are no numbers.  Hindus started marking 1 line, 2 lines, 3 lines for each of the bullocks that entered into cowshed. Lines are okay. But actually 1,2,3 are not. Surprising, isn't it ?

Thou shalt not eat fruit from the tree at the centre. So the Lord commanded. Eve was tempted by serpent and then the original sin was committed. Today manhood so easily sway from one tree to another and count with temptation and greed for the fruits. Jesus commanded to be in his Hypergeometric distribution.  There are some clues when I use Wolfram alpha on Hypergeometric distribution.  

The above is a list of mathematicians admired by Stephen Hawking (on left) and E T Bell (on right)

Have a nice day dear blog readers!!

More thoughts in Delhi

 

I bought a spiral notebook from a stationery shop in Delhi yesterday. Spiral notebook is better because then you can remove a page from the notebook and the notebook doesn't loose significantly. 

I was thinking about hypergeometric functions and hypergeometric distribution.  Consecutive numbers as in (a)^n/(comb((a+1)n,n) and (a)^n/(comb((a-1)n,n) seemed to map hypergeometric functions to hypergeometric distributions in my theory. 

I thought whether 1/2 to 2/3 or 1/2 to 3/4 is of significance? If yes, can it beat the Newton 0 to 1 thing and his approach of approximations?

A student of brain and coming up with a 45 degrees equivalence theory in Maclaurin series is considered brilliant.  And whole heartedly I also feel so. Such student must get rewards of significance and must feel proud and happy . My saint inside swells in pride if this student of great caliber gets an award.

Have a nice day !!

Celebrating Diwali in Delhi

I am in Delhi to celebrate Diwali. My mother is in Ranchi. And I shall join her in two days time.

I have been thinking about hypergeometric functions all the while.

1. The ruler need not be straight.  It could be curved. And curved in 3d.

2. Whether angular momentum concept arises because of 1,x,x squared,  x cubed . . . 

3. Or whether angular momentum arises because of a+1, a+2, . . . 

(I guess because of a+1, a+2, . . . as then it supports Taylor series . This will give fillip to my consecutive numbers concept. If such is the case I can then avoid learning angular momentum and concentrate on consecutive numbers. And also concentrate on differential equations part)

(Rangoli made by my wife here in Delhi)

Indian mathematicians from recent past

Madhava of Sangamagrama,  Ramanujan and Harishchandra. 

Madhava of Sangamagrama is my favorite.  I have nuptial bondage with his thoughts.  He was simple. But he was sure. He was less. But conveyed more. He and Leibniz have a pi by 4 formula. 

Ramanujan had great intuitions.  He was fearless and was sure. He took steps believing in his intuitions,  capacity and in his Vaishnava Lord which guided him. British mathematicians had to consider him as India was ruled by them. Many people think his mathematics base is bogus.  No. I am not with them. Lakshmi consort of Vishnu is goddess of wealth. And wealth are numbers. He must have been good in numbers and most just put him off without reason.

Harishchandra had a dream. To bring mathematics to effort that people put in. A Nehru thought process probably.  It was quite disappointing that he missed winning any prize of distinction. 

I am able to "see" the time,  the light,  the field and the groups. Need to "see" the angular momentum, the differential equations,  the quantum working. I "hope" and "wish" to build my partial differential equations of perfection and as per the Lord's wishes.

Basically the way of a,b,c and z in the hypergeometric functions. So as I see. So as I understand. 

My best wishes.  And have a nice weekend ahead.

Expressions on 10th November 2023

 

Have a nice day !!

Expression on 9th November 2023

 

Have a nice day !!

Expressions on 8th November 2023

 

Have a nice day !!

Kindle book on hypergeometric functions

The cost of the kindle book

The book

My kindle library 

It was necessary to get the kindle book. Because the atmosphere in township of RDCIS is more for hypergeometric functions than my hopes of becoming a comic artist.  Another reason is #Pythashastri,  1,x,x squared,  x cubed.  . . model of mine which is close to hypergeometric distribution and functions. 

I shall spread the expression of the type a^n by combination (bn,cn) summed up from 1 to infinity and allow to be banged by its equivalence to hypergeometric functions. 

Hypergeometric functions are likely to be easy for me. Just like learning advanced calculus to an IITian.

Have a nice day !!