Let be an arbitrary trigonometric polynomial
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with real coefficients, let be a function that is integrable over the interval , and let the th derivative of be bounded in . Then there exists a polynomial for which
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for all , where is the smallest constant possible, known as the th Favard constant.
can be given explicitly by the sum
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which can be written in terms of the Lerch transcendent as
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These can be expressed by
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where is the Dirichlet lambda function and is the Dirichlet beta function. Explicitly,
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