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, 6784Projects:
 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  10.1007/9783030359140_4 ER 
@article{ author = "Cvijović, Đurđe and Pogany, Tibor K.", year = "2020", url = "https://vinar.vin.bg.ac.rs/handle/123456789/8999", 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", title = "Second Type Neumann Series Related to Nicholson’s and to Dixon–Ferrar Formula", pages = "6784", doi = "10.1007/9783030359140_4" }
Cvijović Đ, Pogany TK. Second Type Neumann Series Related to Nicholson’s and to Dixon–Ferrar Formula. Trends in Mathematics. 2020;:6784
Cvijović, Đ.,& Pogany, T. K. (2020). Second Type Neumann Series Related to Nicholson’s and to Dixon–Ferrar Formula. Trends in Mathematics, 6784. https://doi.org/10.1007/9783030359140_4
Cvijović Đurđe, Pogany Tibor K., "Second Type Neumann Series Related to Nicholson’s and to Dixon–Ferrar Formula" (2020):6784, https://doi.org/10.1007/9783030359140_4 .
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