Second Type Neumann Series Related to Nicholson’s and to Dixon–Ferrar Formula
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The second type Neumann series are considered which building blocks are Nicholson’s and the Dixon–Ferrar formulae for (Formula Presented). Related closed form double definite integral expressions are established by using the associated Dirichlet’s series Cahen’s Laplace integral for the Nicholson’s case. However, using Dixon–Ferrar formula a double definite integral expression is again obtained. Certain Open Problems are posed in the last section of the chapter.
Keywords:
Bessel function of the first kind Jν / Bessel function of the second kind Yν / Cahen’s Laplace integral formula / Dixon–Ferrar formula / Integral representation formula / Modified Bessel function of the second kind Kν / Neumann series of Bessel functions / Nicholson’s formulaSource:
Trends in Mathematics, 2020, 67-84Funding / projects:
- NAWA project [PROM PPI/PRO/2018/1/00008]
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VinčaTY - CHAP AU - Cvijović, Đurđe AU - Pogany, Tibor K. PY - 2020 UR - https://vinar.vin.bg.ac.rs/handle/123456789/8999 AB - The second type Neumann series are considered which building blocks are Nicholson’s and the Dixon–Ferrar formulae for (Formula Presented). Related closed form double definite integral expressions are established by using the associated Dirichlet’s series Cahen’s Laplace integral for the Nicholson’s case. However, using Dixon–Ferrar formula a double definite integral expression is again obtained. Certain Open Problems are posed in the last section of the chapter. T2 - Trends in Mathematics T1 - Second Type Neumann Series Related to Nicholson’s and to Dixon–Ferrar Formula SP - 67 EP - 84 DO - 10.1007/978-3-030-35914-0_4 ER -
@inbook{ author = "Cvijović, Đurđe and Pogany, Tibor K.", year = "2020", abstract = "The second type Neumann series are considered which building blocks are Nicholson’s and the Dixon–Ferrar formulae for (Formula Presented). Related closed form double definite integral expressions are established by using the associated Dirichlet’s series Cahen’s Laplace integral for the Nicholson’s case. However, using Dixon–Ferrar formula a double definite integral expression is again obtained. Certain Open Problems are posed in the last section of the chapter.", journal = "Trends in Mathematics", booktitle = "Second Type Neumann Series Related to Nicholson’s and to Dixon–Ferrar Formula", pages = "67-84", doi = "10.1007/978-3-030-35914-0_4" }
Cvijović, Đ.,& Pogany, T. K.. (2020). Second Type Neumann Series Related to Nicholson’s and to Dixon–Ferrar Formula. in Trends in Mathematics, 67-84. https://doi.org/10.1007/978-3-030-35914-0_4
Cvijović Đ, Pogany TK. Second Type Neumann Series Related to Nicholson’s and to Dixon–Ferrar Formula. in Trends in Mathematics. 2020;:67-84. doi:10.1007/978-3-030-35914-0_4 .
Cvijović, Đurđe, Pogany, Tibor K., "Second Type Neumann Series Related to Nicholson’s and to Dixon–Ferrar Formula" in Trends in Mathematics (2020):67-84, https://doi.org/10.1007/978-3-030-35914-0_4 . .
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