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Ramanujan's master theoremLerch zeta functionBeta functionMultiple zeta functionConvex conjugateTheta functionRamanujan primeFourier analysisSpecial values of l-functionsFractional fourier transformLagrange inversion theoremPrime zeta functionResolvent formalismRiemann xi functionAlgebraic number theoryDerivationClass number formulaHartley transformDarboux's theoremArithmetic derivativeDarboux integralRamanujan's sumJacobi methodGraph fourier transformTrace operatorMathieu functionRiemann zeta functionSubderivativeRamanujan summationLegendre's constantDirichlet convolutionAnalytic number theoryGamma functionEuler's continued fraction formulaSchwarz reflection principleEuler's formulaJacobi identityCartan decompositionFractal derivativeFormal derivativeSpectrumRiesz transformMultivariate gamma functionHigher-dimensional gamma matricesKronecker symbolJacobi polynomialsJacobian matrix and determinantLegendre transformationHilbert transformMean value theoremPythagorean trigonometric identityLiouville functionOperator theoryApproximation theoryIncomplete gamma functionSingular integralPentagonal number theoremSymmetric derivativeComplex analysisParseval's identityFrobenius methodIntegration using euler's formulaFredholm integral equationGeneralizations of the derivativeFunctional calculusMultiplication theoremIntegro-differential equationClass field theoryTrigonometric functionsAlgebraic analysisInverse scattering transformDivisor functionMatrix exponentialJacobi eigenvalue algorithmLogarithmic normPoisson summation formulaCotangent complexElliptic operatorHyperbolic functionsLaplace's methodDedekind zeta functionImplicit function theoremGeneralizations of pauli matricesArithmetic combinatoricsConjugate gradient methodSpectral graph theoryQuaternionic analysisNoether's second theoremMatrix sign functionTangent spaceMorse theoryIntegral curveHypercomplex analysisLegendre functionMorera's theoremDelta potentialDifferential equationAnalytic continuationGeneralized continued fractionDirichlet's approximation theorem