Thermal average expansion of moments in small temperature

According to Abramowitz and Stegun eq 9.7.2 the asymptotic form for [Graphics:SoftComptongr217.gif] for larger U is to order [Graphics:SoftComptongr218.gif] is given by the following function

[Graphics:SoftComptongr219.gif]

Let us plot it to see if it works

[Graphics:SoftComptongr220.gif]

[Graphics:SoftComptongr221.gif]

[Graphics:SoftComptongr222.gif]

[Graphics:SoftComptongr223.gif]

[Graphics:SoftComptongr224.gif]

[Graphics:SoftComptongr225.gif]

[Graphics:SoftComptongr226.gif]

[Graphics:SoftComptongr227.gif]

[Graphics:SoftComptongr228.gif]

[Graphics:SoftComptongr229.gif]

[Graphics:SoftComptongr230.gif]

Yes it seems to work!

Expanding the moment for small temperature (I have checked that I have expanded to the lowest order which give the correct series to order [Graphics:SoftComptongr231.gif])

[Graphics:SoftComptongr232.gif]

[Graphics:SoftComptongr233.gif]

[Graphics:SoftComptongr234.gif]

[Graphics:SoftComptongr235.gif]

[Graphics:SoftComptongr236.gif]

[Graphics:SoftComptongr237.gif]

[Graphics:SoftComptongr238.gif]

[Graphics:SoftComptongr239.gif]

[Graphics:SoftComptongr240.gif]

[Graphics:SoftComptongr241.gif]

[Graphics:SoftComptongr242.gif]

[Graphics:SoftComptongr243.gif]

[Graphics:SoftComptongr244.gif]

[Graphics:SoftComptongr245.gif]

[Graphics:SoftComptongr246.gif]

[Graphics:SoftComptongr247.gif]

[Graphics:SoftComptongr248.gif]

[Graphics:SoftComptongr249.gif]

[Graphics:SoftComptongr250.gif]

[Graphics:SoftComptongr251.gif]

[Graphics:SoftComptongr252.gif]

[Graphics:SoftComptongr253.gif]

[Graphics:SoftComptongr254.gif]

[Graphics:SoftComptongr255.gif]

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