Undergrad Series for coth(x/2) via Bernoulli numbers

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SUMMARY

The forum discussion centers on the series representation of coth(x/2) and its relation to Bernoulli numbers as presented in "Guide to Essential Math" by S.M. Blinder. A user questions the validity of equation 7.61, suggesting it may be incorrect. The correct series representation for coth(x/2) is identified as the series for tanh(x/2), clarifying the confusion surrounding the transition in the text.

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  • Understanding of Bernoulli numbers
  • Familiarity with hyperbolic functions, specifically coth and tanh
  • Basic knowledge of mathematical series and their convergence
  • Experience with mathematical notation and terminology
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  • Learn about the derivation of hyperbolic function series
  • Explore the relationship between coth and tanh functions
  • Review mathematical series convergence criteria
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Oppie
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Hello,

I've been using "Guide to Essential Math" by S.M. Blinder from time to time to stay on top of my basic mathematics. I'm currently on the section on Bernoulli Numbers. In that section he has the following (snippet below).

Is the transition to equation 7.61 just wrong? The equation just doesn't make sense. If it is wrong, can anyone "see" what he may have had in mind? What is the "explicit" series equal to if not coth(x/2)? Thank you.

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\coth x =\frac{1}{x}+\frac{x}{3}+...
So why don't you correct (7.61) by yourself ?
 
Oppie said:
What is the "explicit" series equal to if not coth(x/2)?
It's the series for ##\tanh(x/2)##.
 

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