Expansion of Bessel functions of the first kind<i>J</i><sub><i>n</i></sub>(<i>ax</i>) resp. modified Bessel functions of the first kind<i>I</i><sub><i>n</i></sub>(<i>ax</i>) in terms of<i>J</i><sub><i>k</i></sub>(<i>x</i>) · <i>J</i><sub><i>n</i>−<i>k</i></sub>((<i>a</i> − 1)<i>x</i>) resp.<i>I</i><sub><i>k</i></sub>(<i>x</i>) · <i>I</i><sub><i>n</i>−<i>k</i></sub>((<i>a</i> − 1)<i>x</i>), where<i>n</i>,<i>k</i> ∈ ℤ (Q4454054)
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scientific article; zbMATH DE number 2052036
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Expansion of Bessel functions of the first kind<i>J</i><sub><i>n</i></sub>(<i>ax</i>) resp. modified Bessel functions of the first kind<i>I</i><sub><i>n</i></sub>(<i>ax</i>) in terms of<i>J</i><sub><i>k</i></sub>(<i>x</i>) · <i>J</i><sub><i>n</i>−<i>k</i></sub>((<i>a</i> − 1)<i>x</i>) resp.<i>I</i><sub><i>k</i></sub>(<i>x</i>) · <i>I</i><sub><i>n</i>−<i>k</i></sub>((<i>a</i> − 1)<i>x</i>), where<i>n</i>,<i>k</i> ∈ ℤ |
scientific article; zbMATH DE number 2052036 |
Statements
Expansion of Bessel functions of the first kind<i>J</i><sub><i>n</i></sub>(<i>ax</i>) resp. modified Bessel functions of the first kind<i>I</i><sub><i>n</i></sub>(<i>ax</i>) in terms of<i>J</i><sub><i>k</i></sub>(<i>x</i>) · <i>J</i><sub><i>n</i>−<i>k</i></sub>((<i>a</i> − 1)<i>x</i>) resp.<i>I</i><sub><i>k</i></sub>(<i>x</i>) · <i>I</i><sub><i>n</i>−<i>k</i></sub>((<i>a</i> − 1)<i>x</i>), where<i>n</i>,<i>k</i> ∈ ℤ (English)
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7 March 2004
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Bessel function
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modified Bessel function
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