---
title: "Transformations of Heun's Equation and its Integral Relations • CBPF Index"
description: "CBPF INDEX is the system that tracks the scientific and technological output of CBPF. It lists the articles, books, technical reports and other publications of the whole CBPF community."
canonical_url: "https://index.cbpf.br/en/publicacoes/6ad2a767639f62b11adbb2d4"
locale: en
meta:
  "og:description": "CBPF INDEX is the system that tracks the scientific and technological output of CBPF. It lists the articles, books, technical reports and other publications of the whole CBPF community."
  "og:image": "https://index.cbpf.br/_og/d/c_Item%2Ctitulo_Transformations%2Bof%2BHeun's%2BEquation%2Band%2Bits%2BIntegral%2BRelations%2Ctipo_Physics%2BNote%2Ccor_~I2E4MmMwMA%2Cautores_~TMOpYSBKYWNjb3VkIEVsLUphaWNrOyBCYXJ0b2xvbWV1IERvbmF0aWxhIEJvbm9yaW5vIEZpZ3VlaXJlZG8%2Cdetalhe_~MTEvMDEvMjAxMQ%2Csecao_Publications%2Cp_Ii9lbi9wdWJsaWNhY29lcy82YWQyYTc2NzYzOWY2MmIxMWFkYmIyZDQi%2Cs_fXStW3O3Z1KtH_Mp.png"
  "og:image:height": "600"
  "og:image:type": image/png
  "og:image:width": "1200"
  "og:title": "Transformations of Heun's Equation and its Integral Relations • CBPF Index"
  "twitter:image": "https://index.cbpf.br/_og/d/c_Item%2Ctitulo_Transformations%2Bof%2BHeun's%2BEquation%2Band%2Bits%2BIntegral%2BRelations%2Ctipo_Physics%2BNote%2Ccor_~I2E4MmMwMA%2Cautores_~TMOpYSBKYWNjb3VkIEVsLUphaWNrOyBCYXJ0b2xvbWV1IERvbmF0aWxhIEJvbm9yaW5vIEZpZ3VlaXJlZG8%2Cdetalhe_~MTEvMDEvMjAxMQ%2Csecao_Publications%2Cp_Ii9lbi9wdWJsaWNhY29lcy82YWQyYTc2NzYzOWY2MmIxMWFkYmIyZDQi%2Cs_fXStW3O3Z1KtH_Mp.png"
---

> Index of every page on this site: [llms.txt](https://index.cbpf.br/llms.txt)

**Physics Note****Published**

# **Transformations of Heun's Equation and its Integral Relations**

**Léa Jaccoud El-Jaick; Bartolomeu Donatila Bonorino Figueiredo**

01/11/2011

[**Download PDF **0.2 MB](https://index.cbpf.br/files/publicacao/6ad2a767639f62b11adbb2d4/pdf) [**Contact owner**](mailto:apub@cbpf.br?subject=Transformations%20of%20Heun's%20Equation%20and%20its%20Integral%20Relations)

## **Publication details**

<dl>

<dt>Authors</dt>
<dd>Léa Jaccoud El-Jaick; Bartolomeu Donatila Bonorino Figueiredo</dd>

<dt>Type</dt>
<dd>Physics Note</dd>

<dt>Status</dt>
<dd>Published</dd>

<dt>Publication date</dt>
<dd>11/01/2011</dd>

<dt>Description</dt>
<dd>Using the transformation theory for the Heun equation, we find substitutions of variables which preserve the form of the equation for the kernels of integral relations among solutions of the Heun equation. These transformations lead to new kernels for the Heun equation, given by single hypergeometric functions (Lambe-Ward-type kernels) and by products of two hypergeometric functions (Erdélyi-type). Such kernels, by a limiting process, afford new kernels for the confluent Heun equation as well.</dd>

<dt>Year</dt>
<dd>2011</dd>

<dt>Number</dt>
<dd>CBPF-NF-002/11</dd>

<dt>Linked to a thesis</dt>
<dd>No</dd>

<dt>Linked to a grant</dt>
<dd>No</dd>

</dl>

```json
{"@context":"https://schema.org","@graph":[{"@id":"https://index.cbpf.br/en#website","@type":"WebSite","description":"O CBPF INDEX é o sistema de acompanhamento da produção científica e tecnológica do CBPF. Nele é possível obter a lista de publicações de artigos, livros, relatórios técnicos, etc de toda a comunidade do CBPF.","inLanguage":"en-US","name":"CBPF Index","url":"https://index.cbpf.br/en","publisher":{"@id":"https://index.cbpf.br/#identity"},"translationOfWork":{"@id":"https://index.cbpf.br/#website"}},{"@id":"https://index.cbpf.br/en/publicacoes/6ad2a767639f62b11adbb2d4#webpage","@type":"WebPage","description":"CBPF INDEX is the system that tracks the scientific and technological output of CBPF. It lists the articles, books, technical reports and other publications of the whole CBPF community.","name":"Transformations of Heun's Equation and its Integral Relations","url":"https://index.cbpf.br/en/publicacoes/6ad2a767639f62b11adbb2d4","isPartOf":{"@id":"https://index.cbpf.br/en#website"},"potentialAction":[{"@type":"ReadAction","target":["https://index.cbpf.br/en/publicacoes/6ad2a767639f62b11adbb2d4"]}],"primaryImageOfPage":{"@id":"https://index.cbpf.br/#logo"}},{"@id":"https://index.cbpf.br/#identity","@type":"Organization","alternateName":"CBPF","description":"Unidade de pesquisa do Ministério da Ciência, Tecnologia e Inovação dedicada à pesquisa básica em Física, suas aplicações e à formação científica.","email":"web@cbpf.br","legalName":"Centro Brasileiro de Pesquisas Físicas/CBPF","name":"Centro Brasileiro de Pesquisas Físicas","taxID":"04.044.443/0001-35","telephone":"+55-21-2141-7100","url":"https://cbpf.br","address":{"@type":"PostalAddress","streetAddress":"Rua Dr. Xavier Sigaud, 150","addressLocality":"Rio de Janeiro","addressRegion":"RJ","postalCode":"22290-180","addressCountry":"BR"},"logo":{"@id":"https://index.cbpf.br/#logo"},"sameAs":["https://twitter.com/cbpf_mcti"]},{"@id":"https://index.cbpf.br/#logo","@type":"ImageObject","caption":"Centro Brasileiro de Pesquisas Físicas","contentUrl":"https://index.cbpf.br/icon-512x512-light.png","inLanguage":"en-US","url":"https://index.cbpf.br/icon-512x512-light.png"}]}
```

## Sitemap

See the full [sitemap](https://index.cbpf.br/sitemap.md) for all pages.