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janhardo

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11 years, 8 days
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These are questions asked by janhardo

How to plot a 3d Zeta function...

janhardo 335 Maple
complex plotting riemann-zeta
January 21 2022
2 3

Really , the complex plotting possibilities in Maple are difficult to decipher. 

I tried something, but  in general the visualizing for me is not that easy

Now i must look at the complexplot where i got a circle for  the complexplot(sin(x + I), x = -Pi .. Pi) example ?

How to create a plot for the critical li...

janhardo 335
complex plotting riemann-zeta
January 21 2022
1 1

Try to calculate the values for the Zeta(z) on the critical line in symbolic form and also as a plot 

Both i did not yet succeed in 

f:=z->Zeta(z);

complexplot3d(f,-1-1*I..1+1*I);
 

solve(f = 1/2 , z ) 

 

How to get written out some terms of a s...

janhardo 335 Maple
summation inert
January 19 2022
1 5

Alternating serie

 

sum((-1)^(n+1)/(2*n-1), n = 1 .. infinity)

(1/4)*Pi

 (1)

 

> 

sum((-1)^(n + 1)/(2*n - 1), n = 1 .. infinity):

sum((-1)^(n+1)/(2*n-1), n = 1 .. 4)

76/105

 (2)
> 

expand(sum((-1)^(n + 1)/(2*n - 1), n = 1 .. 4),symbolic);

76/105

 (3)
> 

?expand
> 

series(sum((-1)^(n + 1)/(2*n - 1), n = 1 .. infinity),n=0,5);

series((1/4)*Pi,n)

 (4)
> 

 

Info series

   

How to get for n= 4  "for (∑)(((-1)^(n+1))/(2 n-1)) = symbolic term 1+ symbolic term 2+... "

 

 

Download onderzoek_reeks_-hoe_krijg_ik_een_partieke_symbolische_som.mw

How calculating this contour integral...

janhardo 335 Maple
integration contour-integration
January 18 2022
0 10

Contour integration notation

" (∫)[+infinity]^(+infinity)((-x)^(z))/((e)^(x)-1). (ⅆx)/(x)"

 

The limits of integration are intented to indicate a path of integration which begins at + ∞, moves to th e left down the positive real axis, circles the orign once in positive ( counterclockwise) direction, and returns up to the positive real axis to  +∞

-How does this contour look like  in a  graph ?
- the "(ⅆx)/(x)" notation  ?
- calculating this complexe contour integral?

Seems that the concept of the contour integration is similar wit a line integral in real calculus ?

Some more information needed about singularities ( first en second order ..more?)

Nieuwe pagina 1 (hhofstede.nl)

NULL

Download contourintegraal_vraag1.mw

Is 2D input reliable versus 1d maple inp...

janhardo 335 Maple
2dmath
January 16 2022
0 1

I following a example of products multiplication like this one

u:=n->Product(2*k-1,k=1..n)/Product(3*k-1,k=1..n)*x^n;

Calculating with  this with maple 1d input is correct, but when i convert a maple 1d input  to 2D input ( i did somewhere) and use this then there is difference with the maple 1d calculation

Seems to be not a advisable to use converted maple 1d to 2 D input for calculation : ( for a mixed calculation(maple input/2D input)  or solely 2d input) , but only for purpose of seeing what the expression in maple input is standing for.   

Note: i did the calculation again with mixed input and now the correct sequenze of answers shows up ?

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