---
id: hankel
version: "1.2.2"
license: MIT
license_treatment: permissive
maintenance: active
---

# hankel — Hankel Transformations using method of Ogata 2005

License: permissive · Maintenance: active · Downloads: 132.0K/mo

## What it is and what it does

Hankel is a Python library that solves Hankel transforms and integrals—a class of integral transforms needed whenever Fourier analysis must be applied to radially symmetric fields. The core problem it addresses is that standard numerical integration schemes fail on these transforms because Bessel functions oscillate wildly, making quadrature unreliable. The package implements Ogata's method, which locates the zeros of the Bessel function to construct an accurate and fast quadrature scheme.

The library is built on numpy, scipy, and mpmath, and is designed for researchers and engineers working in fields where radial symmetry and Fourier analysis intersect. It supports arbitrary-order transforms, includes built-in support for radially symmetric Fourier transforms, and is thoroughly tested. The package is production-stable, actively maintained, and requires Python 3.6 or later.

Use it for:

- Computing Hankel transforms for wave propagation problems in cylindrically symmetric media.
- Evaluating radially symmetric Fourier transforms in image processing or diffraction analysis.
- Solving integral equations involving Bessel functions in mathematical physics.
- Performing accurate numerical integration of oscillatory functions weighted by Bessel functions.
- Analyzing correlation functions with radial symmetry in statistical applications.

## Worth the install?

AI-flagged interpretation of the facts above — verify before relying.

Computes Hankel transforms and integrals using Ogata's quadrature method, handling the oscillatory nature of Bessel function integration for radially symmetric problems.

Yes. The package solves a specific, well-defined numerical problem (Hankel transforms via Ogata's method) with low install friction, permissive licensing, no known vulnerabilities, active maintenance, and production-stable status. Install it if you need accurate Hankel transforms or radially symmetric Fourier analysis.

## Install

pip install hankel
uv add hankel
poetry add hankel

## Installing hankel

Before you install: Low friction: pure Python wheel with three stable scientific dependencies (numpy, scipy, mpmath). Repository is active with recent commits and production-stable status.

License in practice: MIT license is permissive; you can use, modify, and distribute this package freely with minimal restrictions.

Quickstart:

pip install hankel

import hankel
import numpy as np

# Define a radial function and compute its Hankel transform
h = hankel.HankelTransform(nu=0)
result = h.transform(lambda r: np.exp(-r), k=1.0)

Requires Python 3.6 or later.

Verify before relying:

- Accuracy benchmarks or error bounds for typical use cases beyond the Ogata 2005 reference.
- Performance characteristics (speed, memory) for large-scale or high-order transforms.
- Specific API and class names available in the hankel module for constructing transforms.

## Package facts

- License: MIT (permissive)
- Python support: supports_current
- Install friction: low
- Maintenance: active
- Downloads: 132.0K/month (top 15,000 on PyPI)
- Known vulnerabilities: none known

## Tags

hankel transform, bessel function integration, radially symmetric fourier, ogata quadrature, oscillatory integral, hankel integral computation, numerical-integration, bessel-functions, fourier-analysis

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