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Integral representations for local dilogarithm and trilogarithm functions
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math.NT
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dilogarithmfunctionsintegralrepresentationsintervaltrilogarithmunitapery
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We show new integral representations for dilogarithm and trilogarithm functions on the unit interval. As a consequence, we also prove (1) new integral representations for Apery, Catalan constants, and Legendre chi functions of order 2, 3, (2) a lower bound for the dilogarithm function on the unit interval, (3) new Euler sums.
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