Factorial and gamma API

Returns n! exactly for non-negative integers (BigInt) and falls back to the Lanczos gamma extension Γ(n+1) for fractional or large n. Answers 'What is 10! exactly?', 'What is 0.5! via the gamma function?'.

Price$0.04per request

MethodPOST

Route/v1/gametheory/factorial-gamma

StatusLive

MIME typeapplication/json

Rate limit120/minute

Cache0s public

factorialgammalanczoscombinatoricsbigintmathdiscretefunction

API URLhttps://x402.hexl.dev/v1/gametheory/factorial-gamma

Integration docs

Example request

{
  "n": 10
}

Example response

{
  "n": 10,
  "type": "factorial",
  "value": 3628800,
  "valueExact": "3628800",
  "isExactInteger": true,
  "gamma": "Γ(11)",
  "interpretation": "10! = 3628800."
}

Input schema

{
  "type": "object",
  "required": [
    "n"
  ],
  "properties": {
    "n": {
      "type": "number",
      "examples": [
        10,
        0.5
      ]
    }
  }
}

Output schema

{
  "type": "object",
  "additionalProperties": true
}