enumeratio

@enumeratio/analytic ​

Analytic and special-function extensions for @cortex-js/compute-engine — everything past the combinatorial collections: the Hurwitz-zeta family, Gamma-adjacent functions, elliptic and modular functions, hypergeometric functions, integral transforms, and the symbolic machinery (simplification, function-analysis predicates, ODE/difference-equation solving) that reasons about them. Numeric kernels are the implementation; each head also carries a reference definition in definitions.ts — the same function written as a plain expression over compute-engine's own heads — that doubles as a differential oracle against the kernel.

Usage ​

declareAnalytic(ce) declares everything in one pass. ./definitions exports DEFINITIONS and PRIMITIVE for reading a head's reference expression without declaring the package.

text
HurwitzZeta(2, 1)
// Pi ^ 2 / 6 — reduces to the ordinary zeta at a = 1

Heads ​

Zeta and Dirichlet family — Zeta, HurwitzZeta, LerchPhi, PolyLog, DirichletL, DirichletEta, DirichletBeta, DirichletCharacter, StieltjesGamma, PrimeZetaP, MultiZetaValue, RiemannSiegelZ, RiemannSiegelTheta, RiemannZetaZero, KeiperLiLambda, ClausenCl.

Gamma-adjacent — Gamma, GammaLn, GammaRegularized / InverseGammaRegularized, Beta / BetaRegularized / InverseBetaRegularized, Digamma, PolyGamma, BarnesG / LogBarnesG, BernoulliB, HarmonicNumber, Pochhammer / RisingFactorial, Hyperfactorial, NorlundB, BellY.

Elliptic and modular — the Jacobi elliptic functions (JacobiSN, …), EllipticTheta, IncompleteEllipticPi, ModularJ / KleinInvariantJ, EisensteinG, the Carlson symmetric forms (CarlsonRF, RC, RD, RG, RJ).

Hypergeometric — HypergeometricPFQ, HypergeometricU, Hypergeometric0F1 and the regularized 1F1/2F1/3F2 forms, MeijerG, LambertW, ChebyshevT / ChebyshevU, HermiteH, LaguerreL, LegendrePolynomial, ExpIntegralE, BesselJZero.

Transforms and signals — FourierTransform / InverseFourierTransform, LaplaceTransform / InverseLaplaceTransform, MellinTransform / InverseMellinTransform, HankelTransform, FourierSeries, UnitStep, DiscreteDelta / DiracDelta, SquareWave / SawtoothWave / TriangleWave.

Symbolic and solving — FullSimplify, FunctionExpand, PowerExpand, TrigFactor, Refine under Assuming, Inequality, FindInstance, DSolveValue, DifferenceRoot / DifferentialRoot, SeriesCoefficient, NSum, Minimize / Maximize, and the FunctionDomain family of function-analysis predicates (FunctionContinuous, FunctionMonotonicity, FunctionSingularities, …).

The patches these heads land through (lerch-phi, dirichlet, barnes-g, log-gamma, clausen, stieltjes) live in @enumeratio/ce-patches — see its README for the upstreaming model. (round-places, zeta-hurwitz, polylog-order and polygamma-complex landed in compute-engine 0.141 and were retired.)

Explore ​