Complicated Sum in MatLab

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TheEngineer

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Hello guys!
I hope you can help me with the following problem.
I need to work out how to implement the following equations in Matlab.
The most basic question I have regarding the equations is: What do the two variables below the sigma mean?

Thank you in advance

1652716468629.png
 
TheEngineer said:
Hello guys!
I hope you can help me with the following problem.
I need to work out how to implement the following equations in Matlab.
The most basic question I have regarding the equations is: What do the two variables below the sigma mean?

Thank you in advance

View attachment 32749
Click to expand...
[math]\sum_{i, k = 1}^2 x = \sum_{i = 1}^2 \sum_{k = 1}^2 x[/math]
Is that what you are asking?

-Dan
 
topsquark said:
I don't know about any specific Mathematical conventions but I've seen it all over both my Math and Physics texts.

-Dan
Click to expand...
I must've been reading the wrong kind of text. I interpreted as one sum i.e. i=k=1 and i=k=2, and neglect i=1,k=2 and i=2,k=1. I haven't seen it written like that probably because I don't recall ever having beyond 2 loops notationally. Admittedly, it's more convenient to write for larger index counts.
[math]\sum_{k_1,\dots,k_n}f(k_1,\dots,k_n)[/math]Learned something new. ?
 
BigBeachBanana said:
I must've been reading the wrong kind of text. I interpreted as one sum i.e. i=k=1 and i=k=2, and neglect i=1,k=2 and i=2,k=1. I haven't seen it written like that probably because I don't recall ever having beyond 2 loops notationally. Admittedly, it's more convenient to write for larger index counts.
[math]\sum_{k_1,\dots,k_n}f(k_1,\dots,k_n)[/math]Learned something new. ?
Click to expand...
In Math I typically see things like [math]\sum_{j \in J} f(j)[/math]and such. Much nicer than having to write the limits.

-Dan
 
topsquark said:
In Math I typically see things like [math]\sum_{j \in J} f(j)[/math]and such. Much nicer than having to write the limits.

-Dan
Click to expand...
Wikipedia shows sums like that, and others, including this:

There are also ways to generalize the use of many sigma signs. For example,​
​
{\displaystyle \sum _{i,j}}
is the same as​
​
{\displaystyle \sum _{i}\sum _{j}.}
It doesn't show the form with "i,j=1" on the bottom and a single number on the top, but it seems like a reasonable extension despite some chance of being misunderstood.

I do find that notation (with infinity!) in MathWorld. (See equation 25 and following.)
 
BigBeachBanana said:
You need to provide more context to the equations. Right now it's just an alphabet soup.
Click to expand...
I basically want to calculate the magnetic field strength in various points in space (defined by r and z).
Later on I want to use this information to calculate the coil inductance (equations provided in the paper).
The final output of my MatLab-script will be the coil inductance (scalar) and a plot of the field strength in eachpoint around the coil.


I can provide you the title of the paper i found the equations in:
Calculation of the Magnetic Field Created by a Thick Coil by R. Ravaud, G. Lemerquand.

www.tandfonline.com

Calculation of the Magnetic Field Created by a Thick Coil

This paper presents some reduced analytical expressions of the magnetic field produced by a thick coil with rectangular cross section. The expressions obtained have a fully analytical part and ...
www.tandfonline.com

I hope this helps.

Here is the interesting part:


1653176487477.png

1653176504174.png

1653176518344.png
 
TheEngineer said:
Hello guys!
I hope you can help me with the following problem.
I need to work out how to implement the following equations in Matlab.
The most basic question I have regarding the equations is: What do the two variables below the sigma mean?

Thank you in advance

View attachment 32749
Click to expand...
To me it looks like,

the summation is done with [(i = 1, k=1 &, i+k = 2) , (i = 1, k=2 &, i+k = 3), (i = 2, k=1 &, i+k = 3), (i = 2, k=2 &, i+k = 4)]

- so the leading sign will be alternating for summation

- and rest of the expression is independent of i or j

- and the result of the summation will be Hr = 0 = Hz.

Does everybody AGREE?
 
Last edited by a moderator:
Subhotosh Khan said:
- and rest of the expression is independent of i or j

- and the result of the summation will be Hr = 0 = Hz.
Click to expand...
Thanks for the reply.

The variables in Table 1 depend on i and k, so the result of the summation does not add up to zero.
The magnetic field strength is represented by:
[math]H = \sqrt{H_r^2 + H_z^2}[/math]
 
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