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Feb
1
comment Is there any way to differentiate such function?
Glad it helped @Max Echendu.
Feb
1
comment Is there any way to differentiate such function?
Not as stated but you may rewrite $\;f(n)=H_n=\psi(n+1)+\gamma\;$ with $\gamma$ the Euler constant and $\psi$ the digamma function. $\psi$ is defined in the whole complex plane (minus the negative integers) and $f(n)$ may even be given as a Taylor series with $\zeta(k+1)$ coefficients.
Jan
31
comment Euler gamma function differential
It may be useful to rewrite $\Gamma'(x)$ as $\;\Gamma'(x)=\psi(x)\Gamma(x)\;$ from the definition and the properties of the digamma function.
Jan
30
comment How to solve $\int \frac{\ln{(x^4 + x^2)}}{x^2} \mathrm{d}x$?
Using integration by parts (differentiate $\ln$) and partial fractions is one solution...
Jan
14
awarded  Nice Answer
Jan
13
comment Integral of delta dirac function
+1: neat observation concerning the Dirac distribution. Cheers,
Jan
13
comment Integral of delta dirac function
Yes but you ignore my previous sentence "Should you now choose to ignore the divergence of the integral" : the integral is indeed divergent (this is merely a 'regularization' and the P.V. cancels indeed only the imaginary part).
Jan
13
answered Integral of delta dirac function
Jan
10
revised Quadratic number pattern equation
added 19 characters in body
Jan
10
answered Quadratic number pattern equation
Jan
10
revised Asymptotic expansion of $f(x)= \sum_{n=1}^\infty \frac{\sin nx}{\sqrt{n}}$ at the origin
Expansion
Jan
10
answered Asymptotic expansion of $f(x)= \sum_{n=1}^\infty \frac{\sin nx}{\sqrt{n}}$ at the origin
Jan
6
comment Closed Form for the Integral: $\int_0^1 t^n\log\Gamma(t+a)dt$
Glad it interested you @FofX. Note that Gosper's 'negapolygamma' is in fact defined by $$\psi^{(-n-2)}=(z):=\frac 1{n!}\int_0^z (z-t)^{n}\log\Gamma(t)\,dt$$
Jan
6
comment Closed Form for the Integral: $\int_0^1 t^n\log\Gamma(t+a)dt$
The 1998 paper by Adamchik "Polygamma functions of negative order" may interest you. The answer is given in function of $\psi^{(-n)}(t)$ (integrals of polygamma or "Negapolygamma" in Adamchik 'parlance'). An example using Alpha. Another paper by Espinosa and Moll.
Jan
5
comment Can't find the relationship between two columns of numbers. Please Help
@Torre: I don't use the pro feature so that I can't be sure but data's format may be given here i.e. $data = \{\{12.2, 15\}, \{12.4, 16\}\}$ (not sure of the external $\{\}$ and possibly required spaces ' ' indicated)
Jan
4
comment Can't find the relationship between two columns of numbers. Please Help
@Torre: No I don't and think that you will need many more values... even if only to check that your previsions are right!
Jan
4
comment Can't find the relationship between two columns of numbers. Please Help
@Torre: I don't know... We looked at column A and B and searched a relation between these columns without taking care of the date column but the values at the end (as you noticed) don't follow the same pattern : the $11/13$ we had $B=9.35$ for $A=36.77$ while the $12/8$ we had $B=9.21$ and $A=15.69$ ; the relation is clearly different! Are there only two relations depending of the date? Plenty? Is something else changing continuously or not in the background? Who knows... To see what is really going on you will need to look at the actual process going on (or data covering a larger time range)
Jan
4
awarded  Generalist
Jan
3
comment Can't find the relationship between two columns of numbers. Please Help
Of course you may experiment with alpha (change or add couples...). I found too an online widget by Wolfram (no I am not linked to this society...). Other widgets or tools should help you to get polynomial regression or compute it yourself using matrix. You have the right to experiment and find the most adapted method, this may even be fun!
Jan
3
comment Can't find the relationship between two columns of numbers. Please Help
@Torre: Looking back at my links I notice that I reverted 'linear' and 'others' so that following the linear link would show you $$f(x)=14862.8-4932.17*x+541.004*x^2 -19.5755*x^3$$ For $x=9.322$ this gives $40.49$.