Polylogarithm

great guys , i salute your good answers.........

but sorry, i've problem with my system, i cann't salute you all..

nevertheless.....you all are as good as your efforts...

12 + 3 - 4 + 5 + 67 + 8 + 9 = 100 AND

123 + 4 - 5 + 67 - 89 = 100

COMMON GET GOING.....

Start with the sequence of non-zero digits 123456789. The problem is to place plus or minus signs between them so that the result of thus described arithmetic operation will be 100.

THERE IS ABOUT 13 SOLUTIONS TO IT...

YOUR JOB IS SIMPLE.....

JUST FIND 6 OF THEM.....

AND YES .....

AT LEAST ONE SOLUTION SHOULD INVOLVE FACTORIALS AS WELL!!!

THIS IS A QUESTION ASKED TO ME BY MY COUSION BROTHER...

TILL NOW I HAVE PRODUCED 8 SOLUTIONS.... I POST TWO OF THEM...

this may prove quite interesting for you all........

the reference may give you an idea of how really a non integrable looking function may actually be integrable....

Polylogarithm

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The polylogarithm (also known as de Jonquière's function) is a special function Li_s(z) that is defined by the sum

$\operatorname{Li}_s(z) = \sum_{k=1}^\infty {z^k \over k^s}.$

The above definition is valid for all complex numbers s and z where |z|< 1. The polylogarithm is defined over a larger range of z than the above definition allows by the process of analytic continuation.

The special case s = 1 involves the ordinary natural logarithm (Li₁(z)=-ln(1-z)) while the special cases s = 2 and s = 3 are called the dilogarithm (also referred to as Spence's function) and trilogarithm respectively. The name of the function comes from the fact that it may alternatively be defined as the repeated integral of itself, namely that

$\operatorname{Li}_{s+1}(z) = \int_0^z \frac {\operatorname{Li}_s(t)}{t}dt$

so that the dilogarithm is an integral of the logarithm, and so on. For negative integer values of s, the polylogarithm is a rational function.

The polylogarithm also arises in the closed form of the integral of the Fermi-Dirac distribution and the Bose-Einstein distribution and is sometimes known as the Fermi-Dirac integral or the Bose-Einstein integral. Polylogarithms should not be confused with polylogarithmic functions nor with the offset logarithmic integral which has a similar notation.

recenlty , i'm having a peculiar problem.......i study and study hard ................yet i get 3rd grade marks...recently in my institute test ,i got 27 out of 228.
pls help..

i beg you, i always think i'm done with my studies.but wrong i am...
they said ........
class 11th was tough but it would be easy in 12th..but here in my case...............
i found 11th easy as i scored 88% in school exam and got into the top batch due to my wonderful performance in my institute's reshufling test........

but, from when i have come to 12th. i'm dying and thats killing me...sir ,i have a lot of confidence yet its of no use...i think seriously there's a problem with me..
i sometime cry and cry my heart out....my parents support me.....they make me feel the best but yet , my present situation makes me feel more like making the end of me.........
i don't know what is happening to me...i believe in god so i turn up to you as your stupid,foolish younger brother to help me otherwise i would only break myself.....
i am in pain.its because ,i cann't do i want to...i want to make my parents happy..but.......
i do a lot of thinking on my studies on the concepts..
i also think a lot in the correct direction .....but still ....what i think is correct is wrong...
i don't have any habit of making wild guesses....but yet.................
i work hard ,study,think but still get marks even lesser than those rich kids who do no study.......i know they cheat, but no matter they get better marks and thats imp.
and in the process ,i loose, as people can see only my 10% marks,not the useless 100%effort i put...i have tried it all...meditated, did yoga...studied at nights, studied in early morning...yet i don't know why.
sometimes , in darkness...i think why me??????????...where is ayush?????
i have no choice left...

i always try to solve my problems myself...i'm hard at my heart...but this time it has got me by my neck...its breaking me...and soon i will shatter in pieces...i don't know you can help or not....but , i wanted to tell this to someone......and i chose you...

So you all ....

let me explain...i asked for help to puneet sir...

but he wanted it here so, that he can answer it and all others may also benefit..........

Though i know you all will not have this peculiar problem as mine,then a part of it may......

I stop and stand aside and look at the road i'm tending to...

thank you...

keep smiling................

and , yes one more thing can you explain me what the 5th ques.'s answer mean ...how is it so!!!

keep smiling..........it looks marvellous on your face.....

just six!!!!!!!!!!!!!!
yet, i loved this.
It really required some thinking........
keep it up..........

answering 8 of these just means ..you have a broad thinking...
good subham.......this is required for iit(to think differently)....

lets see , is there someone , who didn't see these ques. before, yet is able to answer all 10 correct................

keep smiling..........it looks marvellous on your face.....

chimansu, it was great!!!
literaly beautiful........................
it aws heart touching.......
i don't care from where you got it............... its touching
good, and guys love your parents, as they are the most beautiful people of the world............

keep smiling as it looks good on your face..............

as easy as anything....but yet, a good try to churn our minds..

keep smiling................

sorry for the mess....why it always happen to me???????????????

keep smiling.

AS SAYING GOES.............."OLD IS GOLD''........

it doesn't matter they are oldies or modern or new, what matters it makes you smile.

so, keep smiling................as it looks beautiful on your face.

wonderful, its really good....keep posting these kind of tricks.
i would've awarded you a salute;but the problem is...........
from my login comp. i 'm not able to do so(pls. belive it),i don't know much about the cause of the problem.......

i even complained to goiit moderator.but , the solution he gave didn't show up with any result..

nevermind,great work..
you would surely know........................
"a compliment is much important than any other thing".

keep smiling as it looks good on your face...............

wonderful,beautiful,great.................
a guiding light like you ,is great.

the smile on your face .....its beautiful..

bless me sir...
and keep enligthening us ..

well akku, nice questions, they got me to think a bit, espescially the proving questions.....
keep on posting such cerebrum questions, and as difficult as possible..

keep smiling as it looks good on your face..

Polylogarithm

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