On Parameter Differentiation for Integral Representations of Associated Legendre Functions
For integral representations of associated Legendre functions in terms of modified Bessel functions, we establish justification for differentiation under the integral sign with respect to parameters. With this justification, derivatives for associated Legendre functions of the first and second kind...
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| Дата: | 2011 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2011
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/147177 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | On Parameter Differentiation for Integral Representations of Associated Legendre Functions / H.S. Cohl // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 24 назв. — англ. |
Репозитарії
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irk-123456789-1471772019-05-16T15:38:01Z On Parameter Differentiation for Integral Representations of Associated Legendre Functions Cohl, H.S. For integral representations of associated Legendre functions in terms of modified Bessel functions, we establish justification for differentiation under the integral sign with respect to parameters. With this justification, derivatives for associated Legendre functions of the first and second kind with respect to the degree are evaluated at odd-half-integer degrees, for general complex-orders, and derivatives with respect to the order are evaluated at integer-orders, for general complex-degrees. We also discuss the properties of the complex function f: C\{−1,1}→C given by f(z)=z/(√(z+1)√(z−1)). 2011 Article On Parameter Differentiation for Integral Representations of Associated Legendre Functions / H.S. Cohl // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 24 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 31B05; 31B10; 33B10; 33B15; 33C05; 33C10 DOI:10.3842/SIGMA.2011.050 http://dspace.nbuv.gov.ua/handle/123456789/147177 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
For integral representations of associated Legendre functions in terms of modified Bessel functions, we establish justification for differentiation under the integral sign with respect to parameters. With this justification, derivatives for associated Legendre functions of the first and second kind with respect to the degree are evaluated at odd-half-integer degrees, for general complex-orders, and derivatives with respect to the order are evaluated at integer-orders, for general complex-degrees. We also discuss the properties of the complex function f: C\{−1,1}→C given by f(z)=z/(√(z+1)√(z−1)). |
| format |
Article |
| author |
Cohl, H.S. |
| spellingShingle |
Cohl, H.S. On Parameter Differentiation for Integral Representations of Associated Legendre Functions Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Cohl, H.S. |
| author_sort |
Cohl, H.S. |
| title |
On Parameter Differentiation for Integral Representations of Associated Legendre Functions |
| title_short |
On Parameter Differentiation for Integral Representations of Associated Legendre Functions |
| title_full |
On Parameter Differentiation for Integral Representations of Associated Legendre Functions |
| title_fullStr |
On Parameter Differentiation for Integral Representations of Associated Legendre Functions |
| title_full_unstemmed |
On Parameter Differentiation for Integral Representations of Associated Legendre Functions |
| title_sort |
on parameter differentiation for integral representations of associated legendre functions |
| publisher |
Інститут математики НАН України |
| publishDate |
2011 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/147177 |
| citation_txt |
On Parameter Differentiation for Integral Representations of Associated Legendre Functions / H.S. Cohl // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 24 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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AT cohlhs onparameterdifferentiationforintegralrepresentationsofassociatedlegendrefunctions |
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2023-05-20T17:26:47Z |
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2023-05-20T17:26:47Z |
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1796153300879409152 |