# Numora Taylor Series Expansion API

> Numora Taylor Series Expansion API is a paid API for AI agents from numormo.vercel.app, paid per call via x402, $0.1/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://numormo.vercel.app/api/calculus/taylor
- Price: $0.1/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-dbef65d1
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_33AVi0JvDc65_aBoKsnxF

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-dbef65d1 -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 server-side symbolic or numerical Taylor series computation without installing a math library. Ideal for AI agents that need polynomial approximations of functions on-the-fly, or when you want human-readable series expansion results with no external dependencies. Prefer over local computation when the agent environment lacks calculus libraries.

## Known failure modes

- Invalid or unparseable function expression in fn field — returns error
- Order is negative or non-integer — returns validation error
- Center point is at a singularity of the function (e.g. ln(x) at x=0) — returns computation error
- Missing required fields fn, order, or center — returns 400-style error
- Very high order requests may produce numerical precision issues

## 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 success flag, a result object containing the Taylor series coefficients and polynomial representation, and a human-readable computation description explaining 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-dbef65d1/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
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