Representasi Deret ke dalam Bentuk Integral Lipat Dua

Siti Julaeha; Arini Soesatyo Putri

doi:10.15575/kubik.v2i1.1473

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Siti Julaeha
Jurusan Matematika, UIN Sunan Gunung Djati Bandung
Indonesia

Arini Soesatyo Putri
Jurusan Matematika, UIN Sunan Gunung Djati Bandung
Indonesia

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Representasi Deret ke dalam Bentuk Integral Lipat Dua

Siti Julaeha^(1*), Arini Soesatyo Putri⁽²⁾

(1) Jurusan Matematika, UIN Sunan Gunung Djati Bandung, Indonesia
(2) Jurusan Matematika, UIN Sunan Gunung Djati Bandung, Indonesia
(*) Corresponding Author

Abstract

Representasi suatu deret ke dalam bentuk lain merupakan salah satu kajian yang terdapat di dalam ilmu matematika. Salah satu representasi yang paling umum digunakan adalah representasi deret ke dalam bentuk integral, yang memungkinkan deret tersebut (khususnya deret tak terhingga) dapat ditentukan nilai atau jumlahnya. Banyak cara untuk merepresentasikan deret ke dalam bentuk integral, diantaranya dengan memanfaatkan ekspansi deret Maclaurin, fungsi khusus integral (fungsi gamma dan beta), serta teorema-teorema yang telah ada sebelumnya. Anthony Sofo [9] dalam kajiannya telah menemukan bentuk deret , yang kemudian akan dikaji bagaimana bentuk integral lipat dua dari deret tersebut di dalam paper ini beserta analisis kekonvergenannya.

Keywords

Deret Maclaurin; Integral Lipat Dua; Integral Euler; Identitas Kombinatorial

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References

Artin. E. The Gamma Function. Holt, Rinehart, dan Winston, New York, 1964.

Bartle. R.G, Sherbert. D.R. Introduction to Real Analysis: Third edition. John Wiley & Sons, USA, 2000.

Edwin. J, Purcell. Kalkulus dan Geometri Analitis: Edisi 5 Jilid 2. Erlangga, Jakarta, 1998.

Goddard. B, Rosen. Kenneth H. Elementary Number Theory and Its Applications, Pearson Addison-Wesley, Boston, 2005.

Kerami. D, Sitanggang. C. Kamus Matematika. Balai Pustaka, Jakarta, 2003.

Kohl. Karen T, H. Moll. Victor. Hypergeometric Function. Journal of Mathematical Sciences, 21: 43-54, Chile, 2011.

Krantz. S.C. The Gamma and Beta Function; Chapter 1. Vieweg, Braunschweig, Jerman, 1998.

Munir. Rinaldi. Matematika Diskrit. Informatika, Bandung, 2005.

Sofo. A. Double Integral Representation of Sums, Journal of Analysis, Vol. 8, 2009.

Sofo, A. General Properties Involving Reciprocals of Binomial Coefficients, Journal of Integer Sequences, Vol. 9, 2006.

Varberg. D, Purcell. Kalkulus: Edisi 9 Jilid 1. Erlangga, Jakarta, 2010.

DOI: https://doi.org/10.15575/kubik.v2i1.1473

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