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Cauchy's integral theoremResidueContour integrationNevanlinna theoryComplex analysisSchwarz reflection principleResidue theoremLagrange inversion theoremHypercomplex analysisLog-cauchy distributionJensen's formulaCauchy's integral formulaArithmetic derivativeLogarithmic derivativeAntiderivativeBlaschke productArgumentInverse function ruleComplex measureDirac delta functionFundamental theorem of calculusRiemann zeta functionBranch cutCauchy principal valueCoarea formulaMorera's theoremAnalytic continuationDarboux integralLogarithmic differentiationMittag-leffler's theoremMeromorphic functionSchwarz lemmaAlternating series testMathematical analysisIntegration by partsResolvent formalismMean value theoremHarnack's curve theoremGeneralized continued fractionLerch zeta functionCauchy-schwarz inequalityLefschetz fixed-point theoremLogarithmic normAlgebraic analysisHolomorphic functionDirect comparison testLambert w functionChain ruleZeta functionIntermediate value theoremEuler's formulaDerivative testGamma functionGradient theoremClosed graph theoremRational functionEntire functionBloch's theoremComplex logarithmDifference quotientTrapezoidal ruleIntegro-differential equationIntegral curveLebesgue integrationCauchy productIntegral calculusImplicit functionPoisson summation formulaSmoothnessHartogs's extension theoremNumber-theoretic functionLogarithmic distributionLaurent seriesLebesgue differentiation theoremComplex differential formIntegral transformMatrix differential equationLogistic functionFunctionalDerivationPolygamma functionDirichlet energyLinear functionConvolution theoremQuotient ruleFractional calculusPrincipal valueRadial curveLogarithmic meanRiemann hypothesisMeasure theoryParametric equationExplicit formulae for l-functionsCauchy problemFunctional analysisProbability-generating functionDerivativeMultiple-scale analysisIntegralNumerical integration