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Thoth Association for Mathematics and Sciences

## We now support LaTeX on our website!

At first, we sample in the ( is odd) equidistant points around :

where is some step.
Then we interpolate points by polynomial

(1)

Its coefficients are found as a solution of system of linear equations:

(2)

Here are references to existing equations: (1), (2).
Here is reference to non-existing equation (??).

Compilation of an expression may be suppressed, showing instead the LaTeX source, by preceding the expression with a !.

For mathematical graphs you may use tikzpicture and pgfplots, e.g. :

Binomial theorem
—————-

Exponential function
——————–

Cauchy&ndash;Schwarz inequality
——————————-

Bayes’ theorem
————–

Euler’s summation formula
————————-
_Theorem._ Euler’s summation formula. _If has a continuous
derivative on the interval , where ,
then_

(3)

_Proof._ Let , . For integers and
in we have

Summing from to we find

Hence,

(4)

Integration by parts gives us

When this is combined with \eqref{summation} we obtain
\eqref{theorem}.

### 3 Responses

1. Kays says:

Let be a positive integer and be the fractional par function, then calculate in closed-form the following Multiple Integral :

2. At first, we sample in the ( is odd) equidistant points around :

where is some step.
Then we interpolate points by polynomial

(1)

Its coefficients are found as a solution of system of linear equations:

(2)

Here are references to existing equations: (1), (2).
Here is reference to non-existing equation (??).

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