Here is what I did
Integral at n = 33.333 (proposed. This formula is okayish if we replace 33.333 by numbers from 5 to 50. The factorials between 10 and 100 can be calculated.)
Actual value of 66.666! ((2*33.333)!)
These are the complete statements on 4.666 thing that I blogged about two days back.
In earlier times people were indiscriminately using negatives of numbers and came up with statements like 2+2=5.
Also during those days mathematicians were contemplating of root of minus 1.
Maclaurin had come up with infinite series of sin(x), cos(x) and also log(x). These do not require 0 factorial (0!). Maclaurin could have managed without 0!.
Euler took upon his shoulders the 0!. He also introduced i, the complex number which is root of minus 1. The e constant was born.
"External " binomial expressions (a+b)^n were made by Newton. Newton used his thumb as 1, as a right triangle and also placed it in ground indicating use of gravity. Three things Newton used his thumb for. He was a super human.
Newton's mathematics were spread on all the areas where the "sun never sets".
X=0 is a sin in mathematics. What to say of polynomials equated to 0. Personally I was looking out for m squared minus m minus 1 sorts of expressions but rarely equated them to zero in mind.
I hope my sins are forgot.
In mathematics I wish to learn partial sums and hypergeometry.
My feelings for expressing myself and nature surrounding us is over. With my earlier blog post.
I wish to buy the following books on drawing.
I have felt many Indian intellectuals involving in zero(0) and zero factorial (0!). These intellectuals feel they are zero(0), as they have absence of ego. But the same gentlemen take decisions and actions of zero factorial (0!). Top decisions and top actions. Number 1 decisions and Number 1 actions.
These intellectuals fail to realize that the zero (0) is of the ruler or scale. Not their internals.
I have been busy with n!, 2n!, ((n+1)(n+2))/2 thoughts and expressions. All these expressions start from 1. There is no zero(0). I suggest Indian intellectuals to take advantage of these expressions and develop models of thought. I feel the results are fascinating and good. I have a e to the power of x and log(x) type of equivalent expressions. Yes, my expressions seem good to me and there is scope of something big. But I need help and guidance and cooperation from Professors. Because the concept may be tough.
You may recall my binomial start from 1 and there are decent expressions.
Only thing is I need help from Indian mathematicians.
Let us forget zero(0) and zero factorial (0!). Let us work with 1. Let us remove confusion.
Google blog friends, if possible help me with a group of mathematical intellectuals. If I can join them, I shall be grateful and thankful.
This is what I meant.
Hope you understood the approximate equivalence (in my case) to the similar e and log relations.
If you want clarifications, do comment below.
It works.
Sigma of (((((n+1)(n+2))/2)^n)/((2n)!)*(1/x)^n, summed up from 0 to infinity equals approximately (4.666)^(1/x). Also sum of ((1/x)^n)/(n(n+1) alternately negated, from 1 to infinity gives (n+1)*ln((n+1)/n)-1. Substituting n as 4.666, 4.666 *2, 4.666*3 . . . gives 0.1, 0.1/2, 0.1/3, .....
Please confirm. It seems amazing. The results.
The results are approximate.
Here are some more details
The results are approximate. But fascinating. Thank you, my Lord, Jesus Christ.
I have typed in MS Word the relevant formulas.
I propose multiplying the LHS of third expression in the just above image by (4.666/5) to get better 0.1/n (RHS) accuracy.
Apart from that I do not recommend any more changes. No changes of 4.66 factor. Also I don't want to invest my mind in exploring the why's of (4.666)^(1/y).
I believe God wants it this way.
For very large values the results are inconsistent. This is because of string theory.
See below the inconsistent result.
Remember the famous
1+2+3+4+.............. =-1/12. Yes. String theory.
I believe it comes negated because of Jesus Christ and Anno Domini time. Mental faculties can't work to this level. But Jesus Christ and his time and the inventions by his followers like pen, paper, calculator makes seeing this phenomenon.
The Euler- Mascheroni constant, gamma made easier to represent with consecutive numbers model. I feel delighted that the Lord above helped me in representing a great concept of gamma very simply.
The expression
You may observe that there is only one 3 consecutive number function in above.
Just one or two days and then there is Weekend. May good things happen and hope you are happy. Have a nice time.
The expression is complicated. I thought let me share the text I typed.
Yesterday I was working on some expressions where in gamma came across. I wanted to isolate and make a new expression of gamma. But I could not.
Today morning I thought let me try with a standard formula for gamma, but with consecutive numbers. I made such an expression. My earlier gamma expressions involve integrals. But this one does not. It involves 3 sigma expressions, one log function and three consecutive numbers function at two places.
Here is the expression.
Have a nice day !!
You may be aware that I am deeply interested in two things. Mathematics and drawing art.
As not much help is coming from the Indian society at large, I have decided to take things on my own and develop my thinking in mathematics and drawing art. Indian societies are possibly of education. And not of scholarships.
Mathematics
I have decided not to go after German, American or other mindsets in mathematics. But develop English sense of mathematics. With journals difficult to get hands on, I have decided to concentrate on the following English books on mathematics.
1. Algebra by Hall and Knight
2. Trigonometry by Loney
3. Calculus by Abbott
4. Pure Mathematics by GHHardy
5. Carr book (Ramanujan followed this book)
Drawing Art
Most of the artists over Internet think of "A Box" as the basic drawing element (Stage 1). But quite frankly, I am unable to internalize it.
I find it easier and in resonance with "A Triangle" as the basis for drawing my artwork.
Yesterday, I thought on the box and triangle issue. And decided on solid triangle. I told myself either perform or perish.
I wanted to apprise my blog readers on the above plans which are totally the final ones.
