[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/CKMS.2003.18.4.781

NOTES ON FORMAL MANIPULATIONS OF DOUBLE SERIES

Choi, June-Sang (Department of Mathematics College of Natural Sciences Dongguk University)

Publication Information

Communications of the Korean Mathematical Society / v.18, no.4, 2003 , pp. 781-789 More about this Journal

Abstract

Formal manipulations of double series are useful in getting some other identities from given ones and evaluating certain summations, involving double series. The main object of this note is to summarize rather useful double series manipulations scattered in the literature and give their generalized formulas, for convenience and easier reference in their future use. An application of such manipulations to an evaluation for Euler sums (in itself, interesting), among other things, will also be presented to show usefulness of such manipulative techniques.

Keywords

double series manipulations; Riemann Zeta function; generalized harmonic numbers; harmonic numbers; Euler sums;

Citations & Related Records

Reference

1	Explicit formulas for Bernoulli polynomials of order n / [ J.Choi ] / Indian J. pure appl. Math.
2	/ [ N.Nielsen ] / Die Gammafunktion
3	Formal manipulations of double series and their applications / [ J.Choi;T.Y.Seo ] / Pusan-Kyongnam Math. J.
4	Explicit evaluation of Euler sums / [ D.Borwein;J.M.Borwein;R.Girgensohn ] / Proc. Edinburgh Math. Soc. DOI
5	/ [ E.D.Rainville ] / Special Functions
6	Remarks on some integrals and series involving the Stirling numbers and ξ(η) / [ Li-Chien Shen ] / Trans. Amer. Math. Soc. DOI ScienceOn
7	/ [ I.J.Schwatt ] / An Introduction to the Operations with Series(2nd ed.)
8	/ [ H.M.Srivastava;J.Choi ] / Series Associated with the Zeta and Related Functions

Reference
Cited By KSCI

1	REMARKS ON A SUMMATION FORMULA FOR THREE-VARIABLES HYPERGEOMETRIC FUNCTION $X_8$ AND CERTAIN HYPERGEOMETRIC TRANSFORMATIONS / [Choi, June-Sang;Rathie, Arjun K.;Harsh, H.;] / East Asian mathematical journal
2	ANOTHER METHOD FOR PADMANABHAM'S TRANSFORMATION FORMULA FOR EXTON'S TRIPLE HYPERGEOMETRIC SERIES X₈ / [Kim, Yong-Sup;Rathie, Arjun Kumar;Choi, June-Sang;] / Communications of the Korean Mathematical Society
3	AN EXTENSION OF THE TRIPLE HYPERGEOMETRIC SERIES BY EXTON / [Lee, Seung-Woo;Kim, Yong-Sup;] / Honam Mathematical Journal
4	NOTE ON STIRLING POLYNOMIALS / [Choi, Junesang;] / Journal of the Chungcheong Mathematical Society
5	q-EXTENSION OF A GENERALIZATION OF GOTTLIEB POLYNOMIALS IN THREE VARIABLES / [Choi, June-Sang;] / Honam Mathematical Journal
6	$q$ -EXTENSION OF A GENERALIZATION OF GOTTLIEB POLYNOMIALS IN TWO VARIABLES / [Choi, Junesang;] / Journal of the Chungcheong Mathematical Society
7	APPELL'S FUNCTION F₁ AND EXTON'S TRIPLE HYPERGEOMETRIC FUNCTION X₉ / [Choi, Junesang;Rathie, Arjun K.;] / The Pure and Applied Mathematics
8	A NEW PROOF OF THE EXTENDED SAALSCHÜTZ'S SUMMATION THEOREM FOR THE SERIES ₄F₃ AND ITS APPLICATIONS / [Choi, Junesang;Rathie, Arjun K.;Chopra, Purnima;] / Honam Mathematical Journal
9	CERTAIN FORMULAS INVOLVING EULERIAN NUMBERS / [Choi, Junesang;] / Honam Mathematical Journal
10	ON A HYPERGEOMETRIC SUMMATION THEOREM DUE TO QURESHI ET AL. / [Choi, Junesang;Rathie, Arjun K.;] / Communications of the Korean Mathematical Society
11	AN EXTENSION OF A KUMMER'S QUADRATIC TRANSFORMATION FORMULA WITH AN APPLICATION / [Choi, Junesang;Rathie, Arjun K.;] / Proceedings of the Jangjeon Mathematical Society
12	Generalization of a Transformation Formula for the Exton's Triple Hypergeometric Series X₁₂ and X₁₇ / [Choi, Junesang;Rathie, Arjun K.;] / Kyungpook Mathematical Journal

Reference

3	June-Sang Choi. (2012) Honam Mathematical Journal q-EXTENSION OF A GENERALIZATION OF GOTTLIEB POLYNOMIALS IN THREE VARIABLES / 34 (3) , 327
3	Junesang Choi. (2013) Honam Mathematical Journal CERTAIN FORMULAS INVOLVING EULERIAN NUMBERS / 35 (3) , 373
2	Junesang Choi. (2012) Journal of the Chungcheong Mathematical Society <img align=middle src='http://ocean.kisti.re.kr/cgi-bin/mimetex.cgi?\small{$q$}' alt='$q$' title='$q$' />-EXTENSION OF A GENERALIZATION OF GOTTLIEB POLYNOMIALS IN TWO VARIABLES / 25 (2) , 253
4	Junesang Choi. (2014) Kyungpook mathematical journal Generalization of a Transformation Formula for the Exton's Triple Hypergeometric Series X12and X17 / 54 (4) , 677
3	Junesang Choi. (2013) Honam Mathematical Journal A NEW PROOF OF THE EXTENDED SAALSCHÜTZ'S SUMMATION THEOREM FOR THE SERIES4F3AND ITS APPLICATIONS / 35 (3) , 407
3	JUNESANG CHOI. (2015) Communications of the Korean Mathematical Society CERTAIN NEW GENERATING RELATIONS FOR PRODUCTS OF TWO LAGUERRE POLYNOMIALS / 30 (3) , 191
1	Seung-Woo Lee. (2010) Honam Mathematical Journal AN EXTENSION OF THE TRIPLE HYPERGEOMETRIC SERIES BY EXTON / 32 (1) , 61
	Amir Hossein Namadchi. (2016) Computers & Structures Explicit dynamic analysis using Dynamic Relaxation method / 175 , 91
1	Praveen Agarwal. (2017) Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Certain q-series identities / 111 (1) , 139
1	Junesang Choi. (2013) The Pure and Applied Mathematics APPELL'S FUNCTION F1AND EXTON'S TRIPLE HYPERGEOMETRIC FUNCTION X9 / 20 (1) , 37
6	Nabiullah Khan. (2017) Comptes Rendus Mathematique A new generalization of Apostol-type Laguerre–Genocchi polynomials / 355 (6) , 607
11	Junesang Choi. (2011) Integral Transforms and Special Functions A generalization of a formula due to Kummer† / 22 (11) , 851
3	Junesang Choi. (2013) Communications of the Korean Mathematical Society ON A HYPERGEOMETRIC SUMMATION THEOREM DUE TO QURESHI ET AL. / 28 (3) , 527
3	Junesang Choi. (2013) Journal of the Chungcheong Mathematical Society NOTE ON STIRLING POLYNOMIALS / 26 (3) , 591
12	(2018) Symmetry Symmetric Identities of Hermite-Bernoulli Polynomials and Hermite-Bernoulli Numbers Attached to a Dirichlet Character χ / 10 (12) , 675
1	Junesang Choi. (2013) Advances in Difference Equations Relations between Lauricella’s triple hypergeometric function F A ( 3 ) ( x , y , z ) and Exton’s function X 8 / 2013 (1)
1579-1505	(2018) Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas A new class of generalized Laguerre–Euler polynomials / (1579-1505)