Silver Ratio and Ability expression

In about a month in past, I have given the Indian society three research concepts. Namely

1. 4.666 or KAAL number

2. Sigma of n/(n+1)! for all factorials including decimals. This I propose the name Ability expression. 

3. ((Combination(2n-1,n)+Combination(2n,n))/(Combination(2(n-1)-1,n-1)+Combination(2(n-1),n-1)) ratio.  This ratio I propose a name of Silver Ratio.

The KAAL number, Ability expression and Silver Ratio are of Wolfram Alpha mainly.

It can be NAKAL- ed by Indian society. (N is Neela, my mother). And improved if improving is possible. 

. . . Off to drawing art now. Bipolar mindset.

Have a nice day !!

Interesting Properties

Combination(2n+1,n) plus Combination(2n,n) gives golden ratio like properties. And also other formulas for Gamma values. 

3.8 or something. 

Have a nice day !!

The Holy Bible

 I have ordered 'The Holy Bible' book from Amazon. 

Thank you,  Internet. 

Have a nice day!!

Kaveri Jet Engine

DRDO is developing Kaveri Jet Engine. This will improve our defense strategies.  India has always maintained a stand of no first attack.

With the systems in place these jet engines will give a fitting reply to enemies.

Jai Bharat hi!!

My grudge in SAIL

There are many things which ruins a career of a well meaning individual.

There are guys in government who thinks Cabinet Secretary is more important than Prime Minister. CBI is more important than Armed Forces. 

In SAIL ED(Works) ruined my life, my career and in fact my alliance proposal too.

Therefore, I asked Google AI a vital question. Here it is.

In continuation to earlier blog post

 

Some decimal factorials

There are three statements below which calculates factorials.  For calculating 17.75!, 0.75! and 17! types. However 17.87634125 etc cannot be calculated. because 0.75 is 3/400. And there are no suitable rational numbers for 0.87634125.

But there are some research scope in this.

My pinboard in office

 

The master forgives

 

Sins and Virtues of Mathematics

Sins of mathematics

 1. x =0

2. Polynomials and other functions equated to zero.

3. Maxima and minima equated to zero

4. Rotating thinking about 0

Virtues of mathematics

1. Appreciating beauty in m^2 -m -1. And not equating to zero

2. Alternately negated polynomials and analyzing them for combination(m,k) *(a)^(m-k) * (b)^(k-m) , with k varying from 1 to m. Not 0 to m.

3. Analyzing equations of the type (x-a)(x-b)........ and considering (1/x -1/a)(1/x-1/b) ......

4. Treating A which is A^1 as A^0.95 or so.

Here is a further extension to the Lord's  way

St. Thomas, patron Saint in Kerala and Tamil Nadu

May the doubts of children get clear in their mathematics, your Holiness !!

My rational analysis of 4.6666 or KAAL number

I must state that KAAL number is a Blog article. It is for internet experience. 

Approximate equivalence is much better than accurate formula.  One cannot complete 1/3. Can one ?

(4.666)^(1/x) formula is okay to me. 0, 1,2 etc are not coming properly.  Support of mathematical minds are needed.

0.1/n formula comes okay. And I claimed String Theory for higher values of n in LHS side. Verification from researchers are needed.

Integrals of 4.666 and treatment of lower value for definite integration should have been avoided by me. It is unofficial. 

I must state this. Ramanujan and his Mock Theta Functions are of much larger strides than my statements. I am sure of this fact. He is my Anna (brother) and it is easy for me to accept this certain fact.

My spirit of God asks me to wander all over India and experience Jesus and his 40 day life.

Thanks for your time. 

சொல்வதை செய்வோம், செய்வதை சொல்வோம்

Former CM of Tamil Nadu Kalaignar M Karunanidhi said " We do what we say and we say what we do". He was a great visionary and a great implementer unparalleled in Indian soil since 1947 to 2025. His legacy will continue to inspire us and drive us to deliver contributions to his economic dreams.

I talked of Approximate Integrals and I made it. Much like what Kalaignar said as above. A very small and a very humble offering from my side to the state of Tamil Nadu. Qayanat Calculus theory.

Here is the latest on 4.666 issue.

Gamma functions list

See, where the world is. And we in India eating gobar.

List of gamma function 

Wolframalpha.com gamma results

Hereby, I present results for Gamma values calculations.

These are Wolfram Alpha results.

And that is product of (2n(2n-1)) for n = m to k

Is gamma(2k+1)/gamma(2m-1)

This is good.

But, but,but these do not get you 7.5! if you put m=1 and n=3.25. 

Reason being product operations happen in steps of one.

Then, how about continuity and product integrals? 🤣🤣🤣

Gamma values with logarithm function

Integral from 0 to infinity of e function gives Gamma values. 

Did you know that logarithm function can also ? So brilliant were mathematicians of yesteryears. In fact there are about 10 Gamma expressions to give gamma values. So present day mathematicians are also not bad either.

Gamma with logarithm function.  6.53 !

Have a nice day !!

Iyers

What is Iyer?

Iyer or Aiyar is a caste in Tamil Nadu. They are Brahmans. They do not eat meat, eggs. They have diary products.

What is caste?

Caste is a social identity. Labourers are given a social identity and are called Shudra caste. Priests are given a social identity and are called Brahman caste. Similarly,  Vaishnav are businessmen and Kshatriyas are warriors.

Which God do Brahman worship?

Iyer Brahman worship Shiva. Iyengar Brahman worship Vishnu.

Who is the top priest in Brahmans?

The top priests of Iyer Brahman are the many Shankaracharyas. Iyengar Brahman do not have top priest as such.

Why are there many Shankaracharyas ?

It is as per Shiva, the God. Shiva's grace, dreams and intuitions to common Brahmans makes possible choosing the Shankaracharyas.  It is something like Dalai Lamas. Dalai Lama are chosen by Buddha. 

What are the common activities of a normal Iyer family?

A normal Iyer family believes in clean and elaborate cooking. Taking bath every day. Doing religious practices.  Indulging in carnatic music and Bharatnatyam, a style of dancing.

Which books do Iyers read ?

Upanishads, Vedas and paeans written by old age saints. 

Do Iyers have divisions in their own caste ?

Yes. The divisions are based on something called gothras. Gothra is the Iyer saint you follow while doing Sandhyavandhanam . My gothra is Gargya gothra. In some way I am north Indian Garg surnamed guys.

Am I a higher Iyer or lower Iyer?

I follow my family members and am a lower Iyer. I am like a Dravidian.

What is Sandhyavandanam ?

Sandhyavandanam are morning,  afternoon and evening prayers of both Iyers and Iyengars. Sandhyavandanam involves recitation of Gayatri mantra. Gayatri mantra is similar to 'La ilaha il Allah Mohammed e rasool ullah' of Muslims. Gayatri mantra is 'Om bhurbhuvaha swahaha tatsavidhurvaranium bhargo devasya dimahihi dhiyo yonaha prachodhayath'

How elaborate could Iyer cooking food can get ?

Very elaborate. Precise recipes. Precise ingredients.  No tasting while cooking. Very clean and ritualistic ladies. And then . . . the ladies get to eat in the end. After everyone had their food. Possibly in the end women eat only rasam or sambhar with their rice. Because other items got finished by men.

Namaste. 

Tea is most suitable

Here are details of the brain of Carl Friedrich Gauss. 

Carl Friedrich Gauss 

If I were his cook, I would have given teas to Gauss sir. Coffee would have made him mad.

Need to study him.

The 0.89 minus 2.88 by n raised to 0.95 formula thing

This blog post is about the lower integral value of 0.89 minus 2.88 by n to the power of 0.95. This may interest the mathematicians. 

If it were 0.89 for n>=5 and less than 10 and 0.88 for n >=20 and n <=60 and then increases to 0.9, 0.91 for n>=80; then it is great.  We do not have to change 2.88 by n to the power of 0.95. So is there a scale for above changes in 0.89 then 0.88 and then 0.90,0.91 ? The answer is YES.

See the screen shots below.

So my theory of lower integral value has approval in common numerals formula. 

How about that ?

Have a nice weekend!!

The results as above.

Happy Sunday folks. Pray to Jesus.

108.726 ! is actually 3.989 into 10 to the power 175.

Integral with 54.363 gives 3.14 into 10 to the power 175.

138.318 ! is actually 3.31 into 10 to the power 237.

Integral with 69.159 gives 2.71 into 10 to the power 237.

The formula 0.899 + ((1/n)-(1/10))*((1/n)-(1/60)) - 2.88/(n^0.95) stays. 

I propose 4.666 as KAAL number. KAAL in Hindi means the times we live in.

This finishes. 

KAAL is Kirtivasan Abhaya Akshaya Lata. My family members. 

Final sample result for n>=20 and n<=100

 The final sample result in the range of 20 to 100 is as given below. I have used the following lower integral value

y = 0.5665 + 0.009027083*x - 0.00009515625*x^2 + 3.072917e-7*x^3 + 3.90625e-10*x^4

I hope you like my integral theory. 😎😎😎

Have a nice weekend, dear blog readers.

Sample result

Below is the sample result from my integral.

Have a nice weekend ahead.

Final 4.666 results

My mind was wavering in the integral part. Then I decided on changing the lower value of integral only. I am not going ahead with correction factors.

Finally,

The integral is okay I think for n = 10 to n=300. I have checked randomly.

Goodbye for now.

Have a nice day !!

My suggestion

 I feel one must avoid complicated expressions and be simple in the integral formula. So this is what I did. I asked Math GPT to simplify the big six degree polynomial (which gives decent results) to a two degree polynomial.

The answer I got was (-0.83 *(x^2) - (0.82)*(x) +16.19)

Today (22 May 2025)

So, there are many assumptions in my thoughts and statements. I work on intuitions. When working on intuitions errors do creep up.

Have a nice day !!

My message

Here is the formulas made on 4.666

And the most latest 2n factorial used and blogged in earlier blog.

Calculating 4.73715 ! with only sigma operation

Here is how one can calculate 4.73715! with my formulas.

I came to know only yesterday using Math GPT. That is height of 'Agyaanatha'. It may not be necessary to use integrals for decimal factorial calculations.

Have a nice day !!

Two results in recent times

 I made two expressions in recent times. One more golden ratio formula. And one n! formula.

Golden ratio formula

n! formula

These I have made in recent few days. I hope you like the above expressions.

Have a nice day !!