Differential Equations Arising from the Generating Function of the (<i>r</i>, <i>β</i>)-Bell Polynomials and Distribution of Zeros of Equations
In this paper, we study differential equations arising from the generating function of the <inline-formula> <math display="inline"> <semantics> <mrow> <mo stretchy="false">(</mo> <mi>r</mi> <mo>,</mo> <mi>β...
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| Format: | Article |
| Language: | English |
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MDPI AG
2019-08-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/7/8/736 |
| _version_ | 1818187303786381312 |
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| author | Kyung-Won Hwang Cheon Seoung Ryoo Nam Soon Jung |
| author_facet | Kyung-Won Hwang Cheon Seoung Ryoo Nam Soon Jung |
| author_sort | Kyung-Won Hwang |
| collection | DOAJ |
| description | In this paper, we study differential equations arising from the generating function of the <inline-formula> <math display="inline"> <semantics> <mrow> <mo stretchy="false">(</mo> <mi>r</mi> <mo>,</mo> <mi>β</mi> <mo stretchy="false">)</mo> </mrow> </semantics> </math> </inline-formula>-Bell polynomials. We give explicit identities for the <inline-formula> <math display="inline"> <semantics> <mrow> <mo stretchy="false">(</mo> <mi>r</mi> <mo>,</mo> <mi>β</mi> <mo stretchy="false">)</mo> </mrow> </semantics> </math> </inline-formula>-Bell polynomials. Finally, we find the zeros of the <inline-formula> <math display="inline"> <semantics> <mrow> <mo stretchy="false">(</mo> <mi>r</mi> <mo>,</mo> <mi>β</mi> <mo stretchy="false">)</mo> </mrow> </semantics> </math> </inline-formula>-Bell equations with numerical experiments. |
| first_indexed | 2024-12-11T23:08:54Z |
| format | Article |
| id | doaj.art-4c74b5704c1d48e5abcac2c78124325e |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-12-11T23:08:54Z |
| publishDate | 2019-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-4c74b5704c1d48e5abcac2c78124325e2022-12-22T00:46:48ZengMDPI AGMathematics2227-73902019-08-017873610.3390/math7080736math7080736Differential Equations Arising from the Generating Function of the (<i>r</i>, <i>β</i>)-Bell Polynomials and Distribution of Zeros of EquationsKyung-Won Hwang0Cheon Seoung Ryoo1Nam Soon Jung2Department of Mathematics, Dong-A University, Busan 604-714, KoreaDepartment of Mathematics, Hannam University, Daejeon 34430, KoreaCollege of Talmage Liberal Arts, Hannam University, Daejeon 34430, KoreaIn this paper, we study differential equations arising from the generating function of the <inline-formula> <math display="inline"> <semantics> <mrow> <mo stretchy="false">(</mo> <mi>r</mi> <mo>,</mo> <mi>β</mi> <mo stretchy="false">)</mo> </mrow> </semantics> </math> </inline-formula>-Bell polynomials. We give explicit identities for the <inline-formula> <math display="inline"> <semantics> <mrow> <mo stretchy="false">(</mo> <mi>r</mi> <mo>,</mo> <mi>β</mi> <mo stretchy="false">)</mo> </mrow> </semantics> </math> </inline-formula>-Bell polynomials. Finally, we find the zeros of the <inline-formula> <math display="inline"> <semantics> <mrow> <mo stretchy="false">(</mo> <mi>r</mi> <mo>,</mo> <mi>β</mi> <mo stretchy="false">)</mo> </mrow> </semantics> </math> </inline-formula>-Bell equations with numerical experiments.https://www.mdpi.com/2227-7390/7/8/736differential equationsBell polynomials<i>r</i>-Bell polynomials(<i>r</i>, <i>β</i>)-Bell polynomialszeros |
| spellingShingle | Kyung-Won Hwang Cheon Seoung Ryoo Nam Soon Jung Differential Equations Arising from the Generating Function of the (<i>r</i>, <i>β</i>)-Bell Polynomials and Distribution of Zeros of Equations Mathematics differential equations Bell polynomials <i>r</i>-Bell polynomials (<i>r</i>, <i>β</i>)-Bell polynomials zeros |
| title | Differential Equations Arising from the Generating Function of the (<i>r</i>, <i>β</i>)-Bell Polynomials and Distribution of Zeros of Equations |
| title_full | Differential Equations Arising from the Generating Function of the (<i>r</i>, <i>β</i>)-Bell Polynomials and Distribution of Zeros of Equations |
| title_fullStr | Differential Equations Arising from the Generating Function of the (<i>r</i>, <i>β</i>)-Bell Polynomials and Distribution of Zeros of Equations |
| title_full_unstemmed | Differential Equations Arising from the Generating Function of the (<i>r</i>, <i>β</i>)-Bell Polynomials and Distribution of Zeros of Equations |
| title_short | Differential Equations Arising from the Generating Function of the (<i>r</i>, <i>β</i>)-Bell Polynomials and Distribution of Zeros of Equations |
| title_sort | differential equations arising from the generating function of the i r i i β i bell polynomials and distribution of zeros of equations |
| topic | differential equations Bell polynomials <i>r</i>-Bell polynomials (<i>r</i>, <i>β</i>)-Bell polynomials zeros |
| url | https://www.mdpi.com/2227-7390/7/8/736 |
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