Some new hybrid power mean formulae of trigonometric sums
Li Chen, Zhuoyu Chen
Abstract
Abstract We apply the analytic method and the properties of the classical Gauss sums to study the computational problem of a certain hybrid power mean of the trigonometric sums and to prove several new mean value formulae for them. At the same time, we also obtain a new recurrence formula involving the Gauss sums and two-term exponential sums.
Topics & Concepts
MathematicsTrigonometryGaussTrigonometric substitutionExponential functionIntegration using Euler's formulaApplied mathematicsDifferentiation of trigonometric functionsGauss sumProofs of trigonometric identitiesMean valueValue (mathematics)Ordinary differential equationQuadratic Gauss sumPure mathematicsMathematical analysisDifferential equationStatisticsBicubic interpolationQuantum mechanicsPolynomialPhysicsLinear interpolationAnalytic Number Theory ResearchMathematical functions and polynomialsAdvanced Mathematical Identities