# Numora Taylor Series Expansion API

> Numora Taylor Series Expansion API is a paid API for AI agents from numormor.netlify.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://numormor.netlify.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-6f7ffd6c
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_JODhkGcQ7uFY4nL7PiF7T

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-6f7ffd6c -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

Use this endpoint when you need a symbolic or numerical Taylor series expansion of a mathematical function around a specific point, especially in pure math, physics simulations, or numerical approximation workflows where no external math library is available and micropayment-based computation is acceptable.

## Known failure modes

- Invalid or unparseable function expression returns error
- Non-integer order value causes validation failure
- Order too high may cause performance or overflow issues
- Missing required fields (fn, order, center) returns 400-style error
- Functions with singularities at the center point may return NaN or error
- Payment not provided or insufficient USDC triggers 402 Payment Required

## 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 containing a success flag, a result object with the Taylor series data (likely coefficients and/or the polynomial expression), and a human-readable computation string describing what was calculated.

## 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-6f7ffd6c/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
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