# Fourier Series Coefficients Calculator API

> For the complete documentation index, see [llms.txt](/llms.txt).

Fourier coefficients a0, a_n and b_n for a function over one period, with amplitude, phase and symmetry detection.

Use this endpoint to add the tool to your app, site, workflow, or agent without rebuilding formulas, validation, examples, and docs.

- Slug: `fourier-series-coefficients-calculator`
- Category: `math`
- Version: `2026-04-22`
- Credits per successful call: 1
- Starts on: free
- Max payload: 65536 bytes
- Privacy mode: `hash_only`
- Available on: free, starter, pro, business, scale
- Browser tool: https://miniwebtool.com/fourier-series-coefficients-calculator/

## Endpoint

`POST https://api.miniwebtool.com/v1/tools/fourier-series-coefficients-calculator/run`

## Request body

| Field | Type | Required | Description |
| --- | --- | --- | --- |
| `expression` | `str` | no | f(x) over one period |
| `period_start` | `float` | no | start of the period |
| `period_end` | `float` | no | end of the period |
| `harmonics` | `int` | no | number of harmonics (1-20) |

## Example request

```json
{
  "expression": "x",
  "period_start": -3.141592653589793,
  "period_end": 3.141592653589793,
  "harmonics": 5
}
```

## cURL

```bash
curl -X POST https://api.miniwebtool.com/v1/tools/fourier-series-coefficients-calculator/run \
  -H 'Authorization: Bearer mwt_live_YOUR_KEY' \
  -H 'Content-Type: application/json' \
  -d '{"expression":"x","period_start":-3.141592653589793,"period_end":3.141592653589793,"harmonics":5}'
```

## Response envelope

```json
{
  "request_id": "01K...",
  "tool": "fourier-series-coefficients-calculator",
  "tool_version": "2026-04-22",
  "credits_used": 1,
  "result": {}
}
```

## Errors

Errors are RFC 7807 `application/problem+json`. Branch on `code`, not `title`.

## MCP

Agents can discover and call this tool through `https://api.miniwebtool.com/mcp` or `https://api.miniwebtool.com/v1/mcp` using MCP `tools/list` and `tools/call`.

## Frequently asked

### What does the Fourier Series Coefficients Calculator API do?

Fourier coefficients a0, a_n and b_n for a function over one period, with amplitude, phase and symmetry detection. Use it to add this utility without rebuilding formulas, validation, examples, and documentation.

### How much does one call cost?

1 credit per successful call. Failed calls do not bill.

### What parameters are required?

Required fields: (none). Full schema at `https://api.miniwebtool.com/v1/openapi.json`.

### Is this deterministic?

Yes. Same input, same output. Tool version: 2026-04-22.