API reference#

See API stability and compatibility for the proposed stable interfaces, experimental interfaces and compatibility policy for the next release.

Every public object is importable from the top-level package, for example from ramanujan_qft import B0, product_integral. The pages below document them by module. Mass inputs are squared masses. The scalar RMT, Mellin, one-loop and dispersive sunset functions return mpmath numbers, with precision controlled by dps (see Precision and numerical checks). The graph evaluators return result objects containing values and diagnostics: the RMT/Taylor series use arbitrary precision, while hybrid integrate_graph uses epsrel/epsabs and float64 estimates with statistical diagnostics.

Ramanujan’s Master Theorem — ramanujan_qft.rmt#

ramanujan_master_theorem()

\(\Gamma(s)\,\varphi(-s)\), the Mellin transform given by the theorem

mellin_numeric()

numerical Mellin transform, for cross-checks

massive_propagator_rmt()

radial integral of a massive propagator in \(D\) dimensions

Product integrals — ramanujan_qft.mellin#

product_integral()

\(\int_0^\infty x^{s-1} f(x)\,g(x)\,dx\) by Mellin residue summation

exponential()

\(e^{-kx}\)

gaussian()

\(e^{-ax^2}\)

bessel_j()

\(J_\nu(bx)\)

cosine()

\(\cos bx\)

sine()

\(\sin bx\)

inverse_power()

\((x+m)^{-v}\)

gaussian_bessel()

\(e^{-ax^2}J_\nu(bx)\)

MellinFunction

a factor described by its Mellin data

SeriesConvergenceError

no valid expansion reaches the accuracy target

One-loop integrals — ramanujan_qft.one_loop#

B0()

two-point function \(B_0(p^2;m_1^2,m_2^2)\)

B0_mob()

equal-mass \(B_0\) from its Method-of-Brackets series

C0()

three-point function \(C_0(0,0,s;m_1^2,m_2^2,m_3^2)\)

C0_mob()

equal-mass \(C_0\) in closed form

bubble_3d()

the finite \(D=3\) two-point function

Two-loop sunset — ramanujan_qft.sunset#

sunset_threshold()

\((m_1+m_2+m_3)^2\)

sunset_im()

\(\operatorname{Im}S(s)\)

sunset_subtracted()

\(S(s)-S(0)-s\,S'(0)\)

sunset_d2()

\(S''(s)\) below threshold

sunset_second_derivative()

Explicit spelling of sunset_d2; a second derivative, not a D=2 integral

Multiloop graphs — ramanujan_qft.multiloop#

ScalarEdge and ScalarGraph describe the topology, masses, powers, and external Euclidean momenta. integrate_graph() evaluates convergent graphs with RMT scale integration and numerical Hepp sectors. See ramanujan_qft.multiloop.

Multivariate sunset series — ramanujan_qft.sunset_rmt#

schwinger_brackets() generates exact exponent matrices and formal Gamma families. compile_sunset_rmt() selects a justified chart for the massive, unit-power \(D=2\) sunset and resolves its colliding poles analytically. integrate_graph_rmt() evaluates the resulting series with arbitrary precision and an analytic tail bound. See Multivariate RMT and exact brackets for the API and Multivariate Ramanujan series for the D=2 sunset for the derivation and strict convergence domains.

Equal-mass continuation — ramanujan_qft.sunset_taylor#

integrate_sunset_taylor() covers the equal-mass D=2 Euclidean sunset, including vacuum, using a separately named Taylor-series method. See Equal-mass sunset Taylor series.

Legacy (version 0.1) interface#

FeynmanMoBSolver, RamanujanContinuationEngine and the modules under ramanujan_qft.core, ramanujan_qft.solvers and ramanujan_qft.utils are kept for backward compatibility; see Legacy interface (version 0.1).