Mixing
Laurent series $frac{e^z}{z^2 -1}$ about $z=1$
1
$begingroup$
Where to start? I know I need to make all the z's into $ z-1 $'s, so $ ecdot e^{z-1} $ and denominator into $ (z-1)(z+1) $, but from there what do I do with the denominator?
complex-analysis laurent-series
edited Jan 23 at 4:43
El borito
666216
asked Jan 23 at 4:14
MinYoung KimMinYoung Kim
907
$endgroup$
add a comment |
1
$begingroup$
Where to start? I know I need to make all the z's into $ z-1 $'s, so $ ecdot e^{z-1} $ and denominator into $ (z-1)(z+1) $, but from there what do I do with the denominator?
complex-analysis laurent-series
edited Jan 23 at 4:43
El borito
666216
asked Jan 23 at 4:14
MinYoung KimMinYoung Kim
907
$endgroup$
2
$begingroup$
I'd write $z=w+1$ and so find the Laurent series of $e^{w+1}/((w+1)^2-1)$ at $w=0$.
$endgroup$
– Lord Shark the Unknown
Jan 23 at 4:16
$begingroup$
Thanks. I just read this sym.lboro.ac.uk/resources/Handout-Laurent.pdf and everything makes sense now. My textbook is very shallow and goes over this topic very quick.
$endgroup$
– MinYoung Kim
Jan 23 at 4:44
add a comment |
1
1
1
$begingroup$
Where to start? I know I need to make all the z's into $ z-1 $'s, so $ ecdot e^{z-1} $ and denominator into $ (z-1)(z+1) $, but from there what do I do with the denominator?
complex-analysis laurent-series
edited Jan 23 at 4:43
El borito
666216
asked Jan 23 at 4:14
MinYoung KimMinYoung Kim
907
$endgroup$
Where to start? I know I need to make all the z's into $ z-1 $'s, so $ ecdot e^{z-1} $ and denominator into $ (z-1)(z+1) $, but from there what do I do with the denominator?
complex-analysis laurent-series
complex-analysis laurent-series
edited Jan 23 at 4:43
El borito
666216
asked Jan 23 at 4:14
MinYoung KimMinYoung Kim
907
edited Jan 23 at 4:43
El borito
666216
asked Jan 23 at 4:14
MinYoung KimMinYoung Kim
907
edited Jan 23 at 4:43
El borito
666216
edited Jan 23 at 4:43
El borito
666216
edited Jan 23 at 4:43
El borito
666216
666216
asked Jan 23 at 4:14
MinYoung KimMinYoung Kim
907
asked Jan 23 at 4:14
MinYoung KimMinYoung Kim
907
asked Jan 23 at 4:14
MinYoung KimMinYoung Kim
907
907
2
$begingroup$
I'd write $z=w+1$ and so find the Laurent series of $e^{w+1}/((w+1)^2-1)$ at $w=0$.
$endgroup$
– Lord Shark the Unknown
Jan 23 at 4:16
$begingroup$
Thanks. I just read this sym.lboro.ac.uk/resources/Handout-Laurent.pdf and everything makes sense now. My textbook is very shallow and goes over this topic very quick.
$endgroup$
– MinYoung Kim
Jan 23 at 4:44
add a comment |
2
$begingroup$
I'd write $z=w+1$ and so find the Laurent series of $e^{w+1}/((w+1)^2-1)$ at $w=0$.
$endgroup$
– Lord Shark the Unknown
Jan 23 at 4:16
$begingroup$
Thanks. I just read this sym.lboro.ac.uk/resources/Handout-Laurent.pdf and everything makes sense now. My textbook is very shallow and goes over this topic very quick.
$endgroup$
– MinYoung Kim
Jan 23 at 4:44
2
2
$begingroup$
I'd write $z=w+1$ and so find the Laurent series of $e^{w+1}/((w+1)^2-1)$ at $w=0$.
$endgroup$
– Lord Shark the Unknown
Jan 23 at 4:16
$begingroup$
I'd write $z=w+1$ and so find the Laurent series of $e^{w+1}/((w+1)^2-1)$ at $w=0$.
$endgroup$
– Lord Shark the Unknown
Jan 23 at 4:16
$begingroup$
Thanks. I just read this sym.lboro.ac.uk/resources/Handout-Laurent.pdf and everything makes sense now. My textbook is very shallow and goes over this topic very quick.
$endgroup$
– MinYoung Kim
Jan 23 at 4:44
$begingroup$
Thanks. I just read this sym.lboro.ac.uk/resources/Handout-Laurent.pdf and everything makes sense now. My textbook is very shallow and goes over this topic very quick.
$endgroup$
– MinYoung Kim
Jan 23 at 4:44
add a comment |
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2
$begingroup$
I'd write $z=w+1$ and so find the Laurent series of $e^{w+1}/((w+1)^2-1)$ at $w=0$.
$endgroup$
– Lord Shark the Unknown
Jan 23 at 4:16
$begingroup$
Thanks. I just read this sym.lboro.ac.uk/resources/Handout-Laurent.pdf and everything makes sense now. My textbook is very shallow and goes over this topic very quick.
$endgroup$
– MinYoung Kim
Jan 23 at 4:44