Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 07/2017, Volume 451, Issue 1, pp. 508 - 523

A class of terminating balanced q-series are investigated. Thirty summation formulae are established by employing Carlitz' inversions and the polynomial...

Basic hypergeometric series | q-Pfaff–Saalschütz theorem | Bailey's well-poised [formula omitted] series identity | Carlitz inversions | Contiguous relations | Polynomial argument | Bailey's well-poised ψ66 series identity | MATHEMATICS | MATHEMATICS, APPLIED | Bailey's well-poised 6 psi 6 series identity | IDENTITIES | BASIC HYPERGEOMETRIC-SERIES | q-Pfaff-Saalschutz theorem | INVERSION

Basic hypergeometric series | q-Pfaff–Saalschütz theorem | Bailey's well-poised [formula omitted] series identity | Carlitz inversions | Contiguous relations | Polynomial argument | Bailey's well-poised ψ66 series identity | MATHEMATICS | MATHEMATICS, APPLIED | Bailey's well-poised 6 psi 6 series identity | IDENTITIES | BASIC HYPERGEOMETRIC-SERIES | q-Pfaff-Saalschutz theorem | INVERSION

Journal Article

Ramanujan Journal, ISSN 1382-4090, 07/2018, Volume 51, Issue 2, pp. 1 - 15

.... We obtain a general summation theorem using a combination of Heine's transformation, the q-Pfaff-Saalschutz theorem and the q-Kummer sum...

Heine transformation | q-Binomial coefficient | q-Kummer sum | q-Pfaff–Saalschutz summation formula | Basic hypergeometric series | Fibonomial and Lucanomial coefficients | MATHEMATICS | q-Pfaff-Saalschutz summation formula

Heine transformation | q-Binomial coefficient | q-Kummer sum | q-Pfaff–Saalschutz summation formula | Basic hypergeometric series | Fibonomial and Lucanomial coefficients | MATHEMATICS | q-Pfaff-Saalschutz summation formula

Journal Article

Afrika Matematika, ISSN 1012-9405, 12/2013, Volume 24, Issue 4, pp. 647 - 664

.... Thirteen transformation theorems are established, which are utilized to derive several reduction and summation formulae for bivariate basic hypergeometric series.

Primary 33D15 | Watson’s q -Whipple transformation | The Sears transformation | The q -Pfaff–Saalschütz summation theorem | Mathematics, general | Mathematics Education | q -Kampé de Fériet series | Mathematics | History of Mathematical Sciences | Basic hypergeometric series | Applications of Mathematics | Secondary 05A15 | The q-Pfaff-Saalschütz summation theorem | Watson's q-Whipple transformation | q-Kampé de Fériet series

Primary 33D15 | Watson’s q -Whipple transformation | The Sears transformation | The q -Pfaff–Saalschütz summation theorem | Mathematics, general | Mathematics Education | q -Kampé de Fériet series | Mathematics | History of Mathematical Sciences | Basic hypergeometric series | Applications of Mathematics | Secondary 05A15 | The q-Pfaff-Saalschütz summation theorem | Watson's q-Whipple transformation | q-Kampé de Fériet series

Journal Article

Turkish Journal of Mathematics, ISSN 1300-0098, 2018, Volume 42, Issue 5, pp. 2699 - 2706

.... Two transformation formulae are established that contain ten summation formulae as consequences.

Abel's lemma on summation by parts | Terminating balanced series q -Pfaff- Saalschütz theorem | Basic hypergeometric series | MATHEMATICS | terminating balanced series q-Pfaff-Saalschutz theorem | BASIC HYPERGEOMETRIC-SERIES | PARTS | SUMMATION | ABELS LEMMA | basic hypergeometric series | INVERSION

Abel's lemma on summation by parts | Terminating balanced series q -Pfaff- Saalschütz theorem | Basic hypergeometric series | MATHEMATICS | terminating balanced series q-Pfaff-Saalschutz theorem | BASIC HYPERGEOMETRIC-SERIES | PARTS | SUMMATION | ABELS LEMMA | basic hypergeometric series | INVERSION

Journal Article

International Journal of Number Theory, ISSN 1793-0421, 07/2017, Volume 13, Issue 6, pp. 1571 - 1577

We prove that, if m , n ≥ 1 and a 1 , … , a m are non-negative integers, then [ a 1 + ⋯ + a m + 1 ] ! [ a 1 ] ! … [ a m ] ! ∑ h = 0 n − 1 q h ∏ i = 1 m h a i ≡...

q -Pfaff-Saalschütz identity | Faulhaber's formula | q -Chu-Vandermonde summation | q -binomial coefficients | MATHEMATICS | q-Pfaff-Saalschutz identity | q-binomial coefficients | q-Chu-Vandermonde summation

q -Pfaff-Saalschütz identity | Faulhaber's formula | q -Chu-Vandermonde summation | q -binomial coefficients | MATHEMATICS | q-Pfaff-Saalschutz identity | q-binomial coefficients | q-Chu-Vandermonde summation

Journal Article

Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 01/2008, Volume 31, Issue 1, pp. 1 - 17

.... Several transformation, reduction and summation formulae on the double q‐Clausen hypergeometric series are derived as consequences. Copyright © 2007 John Wiley & Sons...

Kampé de Fériet function | q‐Pfaff–Saalschütz formula | double q‐Clausen series | q‐Gauss summation theorem | Sears transformations | basic hypergeometric series | Basic hypergeometric series | q-Pfaff- Saalschütz formula | q-Gauss summation theorem | Double q-Clausen series | SUMMATION FORMULAS | MATHEMATICS, APPLIED | KAMPE | 9-J COEFFICIENTS | Kampe de Feriet function | double q-Clausen series | q-Pfaff-Saalschutz formula

Kampé de Fériet function | q‐Pfaff–Saalschütz formula | double q‐Clausen series | q‐Gauss summation theorem | Sears transformations | basic hypergeometric series | Basic hypergeometric series | q-Pfaff- Saalschütz formula | q-Gauss summation theorem | Double q-Clausen series | SUMMATION FORMULAS | MATHEMATICS, APPLIED | KAMPE | 9-J COEFFICIENTS | Kampe de Feriet function | double q-Clausen series | q-Pfaff-Saalschutz formula

Journal Article

7.
Full Text
Terminating q-Kampe de Feriet Series Phi(1:3;lambda)(1:2;mu) and Phi(2:2;lambda)(2:1;mu)

HIROSHIMA MATHEMATICAL JOURNAL, ISSN 0018-2079, 07/2012, Volume 42, Issue 2, pp. 233 - 252

...)-series, we investigate the two terminating q-Kampe de Feriet series Phi(1:3;lambda)(1:2;mu) and Phi(2:2;lambda)(2:1;mu). Several reduction and summation formulae are established...

SUMMATION FORMULAS | TRANSFORMATION | MATHEMATICS | Watson's q-Whipple transformation | The q-Pfaff-Saalschutz summation theorem | The Sears transformation | HYPERGEOMETRIC-SERIES | Basic hypergeometric series | REDUCTION FORMULAS | q-Kampe de Feriet series | q-Kampé de Fériet series | q-Pfaff--Saalschütz summation theorem | 05A15 | 33D15

SUMMATION FORMULAS | TRANSFORMATION | MATHEMATICS | Watson's q-Whipple transformation | The q-Pfaff-Saalschutz summation theorem | The Sears transformation | HYPERGEOMETRIC-SERIES | Basic hypergeometric series | REDUCTION FORMULAS | q-Kampe de Feriet series | q-Kampé de Fériet series | q-Pfaff--Saalschütz summation theorem | 05A15 | 33D15

Journal Article

Electronic Journal of Combinatorics, ISSN 1077-8926, 2011, Volume 18, Issue 2, pp. 1 - 44

.... Using a suitably reformulated version of this identity that we call Euler's Telescoping Lemma, we give alternate proofs of all the key summation theorems for terminating Hypergeometric Series...

Derangements | Q-Chu-Vandermonde sum | Basic Hypergeometric Series | Telescoping | Fibonacci Polynomials | WZ Method | Fibonacci Numbers | Pell Numbers | Q-series | Generalized Hypergeometric Series | Binomial Theorem | Q-Binomial Theorem | Q-Pell numbers | Pfaff-Saalschütz sum | Very-well-poised 6f5 sum | Q-Fibonacci Numbers | Hypergeometric Series | Chu-Vandermonde sum | Q-Dougall summation | Q-Pfaff- Saalschütz sum | q-Binomial Theorem | MATHEMATICS, APPLIED | q-Dougall summation | q-Fibonacci Numbers | SEQUENCES | SUMMATION | HYPERGEOMETRIC-SERIES | q-series | PELL | MATHEMATICS | PENTAGONAL NUMBER THEOREM | q-Chu-Vandermonde sum | STATISTICS | Q-FIBONACCI POLYNOMIALS | TRANSFORMATION FORMULAS | q -Pfaff-Saalschutz sum | ROGERS-RAMANUJAN IDENTITIES | q-Pell numbers | Pfaff-Saalschutz sum | very-well-poised phi sum

Derangements | Q-Chu-Vandermonde sum | Basic Hypergeometric Series | Telescoping | Fibonacci Polynomials | WZ Method | Fibonacci Numbers | Pell Numbers | Q-series | Generalized Hypergeometric Series | Binomial Theorem | Q-Binomial Theorem | Q-Pell numbers | Pfaff-Saalschütz sum | Very-well-poised 6f5 sum | Q-Fibonacci Numbers | Hypergeometric Series | Chu-Vandermonde sum | Q-Dougall summation | Q-Pfaff- Saalschütz sum | q-Binomial Theorem | MATHEMATICS, APPLIED | q-Dougall summation | q-Fibonacci Numbers | SEQUENCES | SUMMATION | HYPERGEOMETRIC-SERIES | q-series | PELL | MATHEMATICS | PENTAGONAL NUMBER THEOREM | q-Chu-Vandermonde sum | STATISTICS | Q-FIBONACCI POLYNOMIALS | TRANSFORMATION FORMULAS | q -Pfaff-Saalschutz sum | ROGERS-RAMANUJAN IDENTITIES | q-Pell numbers | Pfaff-Saalschutz sum | very-well-poised phi sum

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 09/2017, Volume 453, Issue 2, pp. 761 - 772

.... As applications we prove a summation formula for a product of two q-Delannoy numbers along with some congruences for sums involving q-Delannoy numbers...

q-Chu–Vandermonde | q-Pfaff–Saalschütz | q-binomial theorem | q-analogue of Clausen's formula | q-Delannoy numbers | LEGENDRE POLYNOMIALS | MATHEMATICS | MATHEMATICS, APPLIED | q-Pfaff-Saalschutz | HYPERGEOMETRIC-SERIES | SUPERCONGRUENCES | q-Chu-Vandermonde

q-Chu–Vandermonde | q-Pfaff–Saalschütz | q-binomial theorem | q-analogue of Clausen's formula | q-Delannoy numbers | LEGENDRE POLYNOMIALS | MATHEMATICS | MATHEMATICS, APPLIED | q-Pfaff-Saalschutz | HYPERGEOMETRIC-SERIES | SUPERCONGRUENCES | q-Chu-Vandermonde

Journal Article

JOURNAL OF ALGEBRAIC COMBINATORICS, ISSN 0925-9899, 05/2020, Volume 51, Issue 3, pp. 469 - 478

.... Their limiting series are deduced as consequences. The "dual formulae" are also derived by means of the polynomial argument.

MATHEMATICS | Carlitz inversions | COMBINATORIAL IDENTITIES | Heine transformation | HYPERGEOMETRIC-SERIES | Basic hypergeometric series | q-Duplicate inversions | INVERSION TECHNIQUES | Contiguous relations | q-Pfaff-Saalschutz summation theorem | TRANSFORMATIONS

MATHEMATICS | Carlitz inversions | COMBINATORIAL IDENTITIES | Heine transformation | HYPERGEOMETRIC-SERIES | Basic hypergeometric series | q-Duplicate inversions | INVERSION TECHNIQUES | Contiguous relations | q-Pfaff-Saalschutz summation theorem | TRANSFORMATIONS

Journal Article

Springer Proceedings in Mathematics and Statistics, ISSN 2194-1009, 2017, Volume 221, pp. 677 - 692

.... Springer Proceedings in Mathematics & Statistics, vol 221. Springer, Cham We employ a one-variable extension of q-rook theory to give combinatorial proofs of some basic hypergeometric summations, including the q-Pfaff-Saalsch...

Jain summation | Matchings | Alpha-parameter model | q-Pfaff–Saalschütz summation | q-analogues | Rook numbers | Basic hypergeometric series | Mathematics - Combinatorics

Jain summation | Matchings | Alpha-parameter model | q-Pfaff–Saalschütz summation | q-analogues | Rook numbers | Basic hypergeometric series | Mathematics - Combinatorics

Conference Proceeding

RAMANUJAN JOURNAL, ISSN 1382-4090, 06/1999, Volume 3, Issue 2, pp. 175 - 203

.... This allows us to combine the three types of series, and get D-n extensions of the following classical summation and transformation theorems...

MATHEMATICS | q-Whipple transformation | q-Dougall sum | Rogers-Selberg function | q-Pfaff-Saalschutz sum | POISED PHI TRANSFORMATIONS | LEMMA | U(N) | q-Gauss summation | very-well-poised phi sum | multiple basic hypergeometric series related to the root systems A(n), C-n and D-n, U(n+1) series | BAILEY TRANSFORM

MATHEMATICS | q-Whipple transformation | q-Dougall sum | Rogers-Selberg function | q-Pfaff-Saalschutz sum | POISED PHI TRANSFORMATIONS | LEMMA | U(N) | q-Gauss summation | very-well-poised phi sum | multiple basic hypergeometric series related to the root systems A(n), C-n and D-n, U(n+1) series | BAILEY TRANSFORM

Journal Article

The Ramanujan Journal, ISSN 1382-4090, 6/1999, Volume 3, Issue 2, pp. 175 - 203

.... This allows us to combine the three types of series, and get Dn extensions of the following classical summation and transformation theorems...

very-well-poised 6 φ 5 sum | C n and D n | q-Dougall sum | Rogers-Selberg function | Functions of a Complex Variable | q-Pfaff-Saalschütz sum | Field Theory and Polynomials | Mathematics | q-Gauss summation | U(n + 1) series | multiple basic hypergeometric series related to the root systems A n | q-Whipple transformation | Fourier Analysis | Number Theory | Combinatorics | Multiple basic hypergeometric series related to the root systems A | and D | C | Very-well-poised | sum

very-well-poised 6 φ 5 sum | C n and D n | q-Dougall sum | Rogers-Selberg function | Functions of a Complex Variable | q-Pfaff-Saalschütz sum | Field Theory and Polynomials | Mathematics | q-Gauss summation | U(n + 1) series | multiple basic hypergeometric series related to the root systems A n | q-Whipple transformation | Fourier Analysis | Number Theory | Combinatorics | Multiple basic hypergeometric series related to the root systems A | and D | C | Very-well-poised | sum

Journal Article

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