Formula:KLS:09.08:47

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Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \int_{-1}^1(1-x^2)^{-\frac{1}{2}}\ChebyT{m}@{x}\ChebyT{n}@{x}\,dx= \left\{\begin{array}{ll} \displaystyle\frac{\cpi}{2}\,\Kronecker{m}{n}, & n\neq 0\\[5mm] \cpi\,\Kronecker{m}{n}, & n=0 \end{array}\right. }}

Proof

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Symbols List

& : logical and
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \int}}  : integral : http://dlmf.nist.gov/1.4#iv
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle T_{n}}}  : Chebyshev polynomial of the first kind : http://dlmf.nist.gov/18.3#T1.t1.r8
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \delta_{m,n}}}  : Kronecker delta : http://dlmf.nist.gov/front/introduction#Sx4.p1.t1.r4

Bibliography

Equation in Section 9.8 of KLS.

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