Query on indexing to determine coefficients

[bugatti79]

Folks,
I am interested to know what the author is doing in the following

$\displaystyle B_{ij}=EL ij (L)^{(i+j-1)} \left[ \frac{(i-1)(j-1)}{i+j-3} -\frac{2(ij-1)}{i+j-2}+\frac{(i+1)(j+1)}{i+j-1}\right]$

he states that this expression is not valid for $B_{ij}$ when $i=1$ and $j=1,2,...N$

...yet he goes on to actually calculate

$B_{11}=4EIL$, $B_{1j}=B_{j1}=2EIL^j$, $(j>1)$

I understand the the numerator in the first 2 terms inside the big brakets are both 0 when i=j=1 but we still yield a value from the third term...
Any insight will be appreciated
Regards

PS:I notice there is some editing problem with the 3 terms inside the big brackets. There should be a minus and plus separating the terms.

 

[Mark44]

Folks,
I am interested to know what the author is doing in the following

$\displaystyle B_{ij}=EL ij (L)^{(i+j-1)} \left[ \frac{(i-1)(j-1)}{i+j-3} -\frac{2(ij-1)}{i+j-2}+\frac{(i+1)(j+1)}{i+j-1}\right]$

he states that this expression is not valid for $B_{ij}$ when $i=1$ and $j=1,2,...N$

That's not at all obvious. The only restrictions I see are that
1. i + j ≠ 3 (would make the first denominator vanish)
2. i + j ≠ 2 (would make the second denominator vanish)
3. i + j ≠ 1 (would make the third denominator vanish)

...yet he goes on to actually calculate

$B_{11}=4EIL$, $B_{1j}=B_{j1}=2EIL^j$, $(j>1)$

I don't see how. With i = 1, j = 1, the second term in the brackets is 0/0.

I understand the the numerator in the first 2 terms inside the big brakets are both 0 when i=j=1 but we still yield a value from the third term...
Any insight will be appreciated
Regards

PS:I notice there is some editing problem with the 3 terms inside the big brackets. There should be a minus and plus separating the terms.

 

[micromass]

Could you give a link to where you found this question?

 

[bugatti79]

I don't see how. With i = 1, j = 1, the second term in the brackets is 0/0.

Are you saying because one of the terms is indeterminate then the whole equation is invalid and thus cannot be usedt o calcualte $B_{ij}$ for i=j=1?

Could you give a link to where you found this question?

See attached jpeg of question. The answer involves converting the DE into a weak form using a weight function w and splitting the differentiation between the weight function and the dependent variable u.
Would the choice of the approximation functions affect the outcome?

regards