Double and single integrals of the Mittag-Leffler Function: Derivation and Evaluation
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908343235248128 |
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| author | Reynolds, Robert |
| author_facet | Reynolds, Robert |
| contents | One-dimensional and two-dimensional integrals containing $E_b(-u)$ and $E_{α,β}\left(δx^{γ}\right)$ are considered. $E_b(-u)$ is the Mittag-Leffler function and the integral is taken over the rectangle $0 \leq x < \infty, 0 \leq u < \infty$ and $E_{α,β}\left(δx^{γ}\right)$ is the generalized Mittag-Leffler function and the integral is over $0\leq x \leq b$ with infinite intervals explored. A representation in terms of the Hurwitz-Lerch zeta function and other special functions are derived for the double and single integrals, from which special cases can be evaluated in terms of special function and fundamental constants. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_21009 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Double and single integrals of the Mittag-Leffler Function: Derivation and Evaluation Reynolds, Robert General Mathematics Mittag-Leffler function, double integral, Cauchy integral, hypergeometric function One-dimensional and two-dimensional integrals containing $E_b(-u)$ and $E_{α,β}\left(δx^{γ}\right)$ are considered. $E_b(-u)$ is the Mittag-Leffler function and the integral is taken over the rectangle $0 \leq x < \infty, 0 \leq u < \infty$ and $E_{α,β}\left(δx^{γ}\right)$ is the generalized Mittag-Leffler function and the integral is over $0\leq x \leq b$ with infinite intervals explored. A representation in terms of the Hurwitz-Lerch zeta function and other special functions are derived for the double and single integrals, from which special cases can be evaluated in terms of special function and fundamental constants. |
| title | Double and single integrals of the Mittag-Leffler Function: Derivation and Evaluation |
| topic | General Mathematics Mittag-Leffler function, double integral, Cauchy integral, hypergeometric function |
| url | https://arxiv.org/abs/2504.21009 |