# Maclaurin series

My homework question is about the first law of blackbody radiation. I have to prove an expansion when
for KT≫ℏw.
After some rewriting of the formula i have (ex-1)-1

because KT≫ℏw, x is close to zero, so i think i should use the maclaurin series.

According Wolfram Alpha the series expansion is [PLAIN]http://www5b.wolframalpha.com/Calculate/MSP/MSP32441h2h6354114hd8ba00002hih32dh1h5ch337?MSPStoreType=image/gif&s=14&w=174.&h=59. [Broken] [Broken] and this is exactly what i have to prove. But i have no idea how to come here. I tried to use all my knowledge but i don't even come close to the expansion that it should be...

So my question is: what are the steps from (ex-1)-1 to [PLAIN]http://www5b.wolframalpha.com/Calculate/MSP/MSP32441h2h6354114hd8ba00002hih32dh1h5ch337?MSPStoreType=image/gif&s=14&w=174.&h=59. [Broken] [Broken]

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PeroK
Homework Helper
Gold Member
2020 Award
My homework question is about the first law of blackbody radiation. I have to prove an expansion when
for KT≫ℏw.
After some rewriting of the formula i have (ex-1)-1

because KT≫ℏw, x is close to zero, so i think i should use the maclaurin series.

According Wolfram Alpha the series expansion is [PLAIN]http://www5b.wolframalpha.com/Calculate/MSP/MSP32441h2h6354114hd8ba00002hih32dh1h5ch337?MSPStoreType=image/gif&s=14&w=174.&h=59. [Broken] [Broken] and this is exactly what i have to prove. But i have no idea how to come here. I tried to use all my knowledge but i don't even come close to the expansion that it should be...

So my question is: what are the steps from (ex-1)-1 to [PLAIN]http://www5b.wolframalpha.com/Calculate/MSP/MSP32441h2h6354114hd8ba00002hih32dh1h5ch337?MSPStoreType=image/gif&s=14&w=174.&h=59. [Broken] [Broken]

First, find the expansion for ##e^x - 1##. Then think Binomial.

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Mark44
Mentor
My homework question is about the first law of blackbody radiation. I have to prove an expansion when
for KT≫ℏw.
After some rewriting of the formula i have (ex-1)-1

because KT≫ℏw, x is close to zero, so i think i should use the maclaurin series.

According Wolfram Alpha the series expansion is [PLAIN]http://www5b.wolframalpha.com/Calculate/MSP/MSP32441h2h6354114hd8ba00002hih32dh1h5ch337?MSPStoreType=image/gif&s=14&w=174.&h=59. [Broken] [Broken] and this is exactly what i have to prove. But i have no idea how to come here. I tried to use all my knowledge but i don't even come close to the expansion that it should be...

So my question is: what are the steps from (ex-1)-1 to [PLAIN]http://www5b.wolframalpha.com/Calculate/MSP/MSP32441h2h6354114hd8ba00002hih32dh1h5ch337?MSPStoreType=image/gif&s=14&w=174.&h=59. [Broken] [Broken]
What do KT and ℏw have to do with (ex - 1)-1?

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