# API reference

See {doc}`/API_STABILITY` 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 {doc}`/user_guide/precision`). 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`

| | |
|---|---|
| {py:func}`~ramanujan_qft.rmt.ramanujan_master_theorem` | $\Gamma(s)\,\varphi(-s)$, the Mellin transform given by the theorem |
| {py:func}`~ramanujan_qft.rmt.mellin_numeric` | numerical Mellin transform, for cross-checks |
| {py:func}`~ramanujan_qft.rmt.massive_propagator_rmt` | radial integral of a massive propagator in $D$ dimensions |

## Product integrals — `ramanujan_qft.mellin`

| | |
|---|---|
| {py:func}`~ramanujan_qft.mellin.product_integral` | $\int_0^\infty x^{s-1} f(x)\,g(x)\,dx$ by Mellin residue summation |
| {py:func}`~ramanujan_qft.mellin.exponential` | $e^{-kx}$ |
| {py:func}`~ramanujan_qft.mellin.gaussian` | $e^{-ax^2}$ |
| {py:func}`~ramanujan_qft.mellin.bessel_j` | $J_\nu(bx)$ |
| {py:func}`~ramanujan_qft.mellin.cosine` | $\cos bx$ |
| {py:func}`~ramanujan_qft.mellin.sine` | $\sin bx$ |
| {py:func}`~ramanujan_qft.mellin.inverse_power` | $(x+m)^{-v}$ |
| {py:func}`~ramanujan_qft.mellin.gaussian_bessel` | $e^{-ax^2}J_\nu(bx)$ |
| {py:class}`~ramanujan_qft.mellin.MellinFunction` | a factor described by its Mellin data |
| {py:class}`~ramanujan_qft.mellin.SeriesConvergenceError` | no valid expansion reaches the accuracy target |

## One-loop integrals — `ramanujan_qft.one_loop`

| | |
|---|---|
| {py:func}`~ramanujan_qft.one_loop.B0` | two-point function $B_0(p^2;m_1^2,m_2^2)$ |
| {py:func}`~ramanujan_qft.one_loop.B0_mob` | equal-mass $B_0$ from its Method-of-Brackets series |
| {py:func}`~ramanujan_qft.one_loop.C0` | three-point function $C_0(0,0,s;m_1^2,m_2^2,m_3^2)$ |
| {py:func}`~ramanujan_qft.one_loop.C0_mob` | equal-mass $C_0$ in closed form |
| {py:func}`~ramanujan_qft.one_loop.bubble_3d` | the finite $D=3$ two-point function |

## Two-loop sunset — `ramanujan_qft.sunset`

| | |
|---|---|
| {py:func}`~ramanujan_qft.sunset.sunset_threshold` | $(m_1+m_2+m_3)^2$ |
| {py:func}`~ramanujan_qft.sunset.sunset_im` | $\operatorname{Im}S(s)$ |
| {py:func}`~ramanujan_qft.sunset.sunset_subtracted` | $S(s)-S(0)-s\,S'(0)$ |
| {py:func}`~ramanujan_qft.sunset.sunset_d2` | $S''(s)$ below threshold |
| {py:func}`~ramanujan_qft.sunset.sunset_second_derivative` | Explicit spelling of `sunset_d2`; a second derivative, not a D=2 integral |

## Multiloop graphs — `ramanujan_qft.multiloop`

{py:class}`~ramanujan_qft.multiloop.ScalarEdge` and
{py:class}`~ramanujan_qft.multiloop.ScalarGraph` describe the topology, masses,
powers, and external Euclidean momenta.
{py:func}`~ramanujan_qft.multiloop.integrate_graph` evaluates convergent graphs
with RMT scale integration and numerical Hepp sectors. See {doc}`multiloop`.

## Multivariate sunset series — `ramanujan_qft.sunset_rmt`

{py:func}`~ramanujan_qft.brackets.schwinger_brackets` generates exact exponent
matrices and formal Gamma families. {py:func}`~ramanujan_qft.sunset_rmt.compile_sunset_rmt`
selects a justified chart for the massive, unit-power $D=2$ sunset and resolves
its colliding poles analytically. {py:func}`~ramanujan_qft.sunset_rmt.integrate_graph_rmt`
evaluates the resulting series with arbitrary precision and an analytic tail
bound. See {doc}`sunset_rmt` for the API and {doc}`/user_guide/sunset_rmt` for
the derivation and strict convergence domains.

## Equal-mass continuation — `ramanujan_qft.sunset_taylor`

{py:func}`~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 {doc}`sunset_taylor`.

## 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 {doc}`legacy`.

```{toctree}
:hidden:
:maxdepth: 1

rmt
mellin
one_loop
sunset
multiloop
sunset_rmt
sunset_taylor
legacy
```