Error in Mathematical Methods for Physicist by Arfken, et al

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SUMMARY

The discussion identifies three specific errors in the textbook "Mathematical Methods for Physicists: A Comprehensive Guide (Seventh Edition)" by Arfken, Weber, and Harris. The first error is in Equation 1.15 on page 8, where the symbol ≤ is incorrectly used instead of <. The second error is in Exercise 1.1.7 on page 11, which lacks the prerequisite conditions that p > 0 and q > 0. Lastly, in Equation 1.66 on page 34, the statement regarding the convergence of the power series is incorrect, as it fails to account for the conditions under which the ratio test applies.

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Mathematical Methods for Physicist: A Comprehensice Guide (Seventh Edition) by George Brown Arfken, Hans Jürgen Weber, Frank E. Harris

I am studying it.
Up to now I read to page 35 and have found 3 errors.

Chapter 1 Mathematical Preliminaries
1.1 Infinite Series
More Sensitive Tests
Equation 1.15 (Page 8)
≤ is incorrect, < is correct.

Exercises 1.1.7 (Page 11)
It must be given to prerequisite that p > 0 and q > 0

1.3 Binomial Theorem
Equation 1.66 (Page 34)
If n > m, m(m - 1)...(m - n + 1) = 0
In other words, whether n → ∞ or not, the remainder is always 0.
Furthermore, the radius (interval) of convergence is not -1 < x < 1.
Because m(m - 1)...(m - n + 1) = 0, ratio test fail.
As far as either m or x does not approach infinity, the power series is convergent.
 
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I don’t get the point of this thread. Do you have questions regarding these issues? Otherwise errors in textbooks are nothing new as it is essentially impossible to write an error-free text. In particular one with the size of Arfken.
 
Maybe the errors are deliberate. Put there to make sure you're paying attention.
 
Jehannum said:
Maybe the errors are deliberate. Put there to make sure you're paying attention.
Being a textbook author myself, I seriously doubt this. It would be quite non-pedagogical.
 
I imagine the edition I used (back in the day) had even more errors. (No wonder I'm so confused!)
 

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