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a question about chebyshev polynomials in a crack problem

I use the chebyshev polynomials to solve the singular integral equation of a crack problem. I encountered a problem that when Chebyshev polynomials are truncated  at the even order, the results are convergent. However, if the polynomials are truncated at the odd order, the results are not convergent. Does anybody have any idea about this?  Thanks a lot.

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