# Numora Taylor Series Expansion

> Numora Taylor Series Expansion is a paid API for AI agents from numorapoi.orbonomy.xyz, paid per call via x402, $0.04/call, status unknown (last checked 2026-09-14).

Computes the Taylor series expansion of a mathematical function around a specified center point up to a given order

## Facts

- Endpoint: POST https://numorapoi.orbonomy.xyz/api/calculus/taylor
- Price: $0.04/call
- Payment: x402
- Status: unknown
- Last checked: 2026-09-14
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/numora-taylor-series-expansion-api-9acc9ebc
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_jvPdfAtRV8KlFO6dMBv5F

Status and success rate cover calls made through Zero and Zero's own probes. Third-party monitors may report differently.

## How to call it through Zero

Zero handles the 402 payment challenge and records the run. With the Zero CLI installed (`npm i -g @zeroxyz/cli`):

```sh
zero fetch --capability numora-taylor-series-expansion-api-9acc9ebc -d '<json body>'
```

Example prompt: Can you compute the Taylor series expansion of sin(x) centered at 0 up to order 6?

## When to prefer this

Choose this endpoint when you need a symbolic or numeric Taylor/Maclaurin series expansion of a mathematical function with no external library dependencies. Ideal for AI agents needing on-demand calculus computations without setting up a local math environment. Prefer over general-purpose code execution when you want a clean, structured JSON result with zero setup.

## Known failure modes

- Invalid or unparseable function expression in 'fn' — returns error or success:false
- Non-integer or negative order value — schema validation failure
- Center point outside the domain of the function (e.g. ln(x) centered at 0) — mathematical domain error
- Payment failure via x402 micropayment — 402 Payment Required response
- Malformed request body missing required fields — 400 Bad Request

## How this service works

100 pure math computation endpoints for AI agents. Statistics, financial math, linear algebra, equation solving, calculus, number theory, sequence generation, and unit conversions. Zero external dependencies. x402 micropayments on Base.

## Output

Returns a JSON object with success status, a result object containing the Taylor series data (coefficients, terms, or polynomial representation), and a human-readable computation string describing what was computed.

## Request schema (JSON Schema)

```json
{
 "type": "object",
 "required": [
  "fn",
  "order",
  "center"
 ],
 "properties": {
  "fn": {
   "type": "string"
  },
  "order": {
   "type": "integer"
  },
  "center": {
   "type": "number"
  }
 }
}
```

## Response schema (JSON Schema)

```json
{
 "type": "object",
 "required": [
  "success",
  "result",
  "computation"
 ],
 "properties": {
  "result": {
   "type": "object",
   "description": "Computation result varies by endpoint"
  },
  "success": {
   "type": "boolean",
   "description": "Always true on success"
  },
  "computation": {
   "type": "string",
   "description": "Human-readable description of what was computed"
  }
 }
}
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/numora-taylor-series-expansion-api-9acc9ebc/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from numorapoi.orbonomy.xyz](https://www.zero.xyz/host/numorapoi.orbonomy.xyz/llms.txt)