# Numora Taylor Series Expansion

> Numora Taylor Series Expansion is a paid API for AI agents from numomo.vercel.app, paid per call via x402, $0.1/call, status unknown (last checked 2026-09-16).

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

## Facts

- Endpoint: POST https://numomo.vercel.app/api/calculus/taylor
- Price: $0.1/call
- Payment: x402
- Status: unknown
- Last checked: 2026-09-16
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/numora-taylor-series-expansion-ba5f9fb3
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_rwEa3zDfG6YVx5zqsV-tP

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-ba5f9fb3 -d '<json body>'
```

Example prompt: Compute the Taylor series expansion of sin(x) centered at 0 up to order 6 for me.

## When to prefer this

Choose this endpoint when you need a pure server-side mathematical Taylor series computation without installing any local math library. Ideal for AI agents that need polynomial approximations of functions on-the-fly, for numerical analysis pipelines, physics simulations, or control system design where a symbolic or numeric Taylor expansion is required. Prefer this over general-purpose code execution when you want a lightweight, single-purpose calculus result with no setup overhead.

## Known failure modes

- Invalid or unparseable function expression string returns an error
- Non-integer or negative order value causes validation failure
- Expansion at a singularity of the function (e.g., ln(x) at x=0) may return an error or undefined result
- Missing required fields (fn, order, center) result in a 400-level error
- Payment failure via x402 protocol blocks request from being processed

## 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 a 'result' containing Taylor series coefficients and/or the polynomial expression, a 'success' boolean, and a 'computation' string describing what was computed in human-readable form.

## 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-ba5f9fb3/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from numomo.vercel.app](https://www.zero.xyz/host/numomo.vercel.app/llms.txt)