User guide

• Ramanujan’s Master Theorem
  • The theorem
  • Using ramanujan_master_theorem
  • Checking a result with mellin_numeric
  • Dimensional regularisation: massive_propagator_rmt
  • Pitfalls: when the theorem does not apply
  • Products of functions
  • See also
• Product integrals by Mellin residue summation
  • A first example
  • The atlas
  • How it works
  • Options
  • Errors and refusals
  • More examples
  • Performance
  • Defining new factors
  • See also
• One-loop integrals
  • B0
  • B0_mob: the Method-of-Brackets series
  • C0
  • C0_mob: the equal-mass closed form
  • bubble_3d: the D = 3 bubble
  • Errors
  • Cost
  • Validation
  • See also
• Two-loop sunset
  • The imaginary part
  • The subtracted sunset
  • The second derivative
  • Cost
  • Errors and limitations
  • Validation
  • See also
• Massive Euclidean multiloop graphs
  • Installation and first calculation
  • Conventions and supported domain
  • Where Ramanujan’s theorem enters
  • Sector integration and errors
  • Validation and path to broader coverage
• Multivariate Ramanujan series for the D=2 sunset
  • Use it
  • Exact graph-to-bracket compilation
  • Proven series regions
  • Pole collisions and finite coefficients
  • Tail bounds and numerical checks
  • Validation and remaining work
• Inspect and export an RMT calculation
  • From graph to series
  • Encoding and schema
  • Refusals remain visible
• Equal-mass sunset: vacuum and Euclidean continuation
  • Derivation and normalization
  • Arithmetic stability and validation
• Precision and numerical checks
  • Requesting digits
  • Printing high-precision results
  • Inputs are exact numbers
  • Precision checks for the Feynman integrals
  • Error control in product_integral
  • What the errors mean
  • Cost and precision
• Conventions
  • Kinematics
  • Loop measure and dimension
  • The UV pole of B0
  • The three-point function
  • The two-loop sunset
  • Signs of imaginary parts
  • Converting to other normalisations
  • Units and numbers