X
Search Filters
Format Format
Subjects Subjects
Subjects Subjects
X
Sort by Item Count (A-Z)
Filter by Count
mathematics (169) 169
11b65 (140) 140
mathematics, applied (61) 61
mathematics, general (54) 54
binomial coefficients (46) 46
number theory (46) 46
combinatorics (45) 45
05a10 (40) 40
mathematics - number theory (38) 38
field theory and polynomials (33) 33
fourier analysis (33) 33
functions of a complex variable (33) 33
05a19 (29) 29
congruences (27) 27
analysis (23) 23
mathematics - combinatorics (23) 23
11a07 (20) 20
mathematical analysis (20) 20
applications of mathematics (19) 19
sums (19) 19
33d15 (18) 18
05a30 (17) 17
numbers (15) 15
polynomials (14) 14
11b68 (13) 13
identities (13) 13
integers (13) 13
integrals (13) 13
primary 11b65 (13) 13
secondary 05a10 (13) 13
congruence (12) 12
series (12) 12
05a15 (11) 11
q-series (11) 11
11b83 (10) 10
33c20 (10) 10
mathematics - classical analysis and odes (10) 10
bernoulli numbers (9) 9
combinatorial analysis (9) 9
ordinary differential equations (9) 9
secondary 11b65 (9) 9
11b75 (8) 8
basic hypergeometric series (8) 8
catalan numbers (8) 8
factorial (8) 8
generating function (8) 8
11f27 (7) 7
11p81 (7) 7
applied mathematics (7) 7
central binomial coefficients (7) 7
convex and discrete geometry (7) 7
formulas (7) 7
functions (7) 7
mathematical modeling and industrial mathematics (7) 7
partitions (7) 7
representations (7) 7
supercongruences (7) 7
transforms (7) 7
11b37 (6) 6
41a60 (6) 6
asymptotic expansion (6) 6
binomial coefficient (6) 6
binomials (6) 6
harmonic numbers (6) 6
hypergeometric functions (6) 6
hypergeometric series (6) 6
identity (6) 6
sequences (6) 6
texts (6) 6
theorems (6) 6
05a17 (5) 5
11b39 (5) 5
11f11 (5) 5
33b15 (5) 5
algebra (5) 5
algebra and number theory (5) 5
coefficients (5) 5
cyclotomic polynomial (5) 5
inequalities (5) 5
rogers-ramanujan identities (5) 5
sun (5) 5
05a20 (4) 4
1/pi (4) 4
11b73 (4) 4
11e25 (4) 4
11f20 (4) 4
11m06 (4) 4
appell-lerch sums (4) 4
calculus (4) 4
catalan number (4) 4
central binomial coefficient (4) 4
china (4) 4
difference equations (4) 4
discrete mathematics and combinatorics (4) 4
factorials (4) 4
fibonacci numbers (4) 4
gamma function (4) 4
markov analysis (4) 4
mathematical functions (4) 4
mock theta functions (4) 4
more...
Language Language
Publication Date Publication Date
Click on a bar to filter by decade
Slide to change publication date range


Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 01/2016, Volume 433, Issue 1, pp. 706 - 711
We prove the last remaining case of the original 13 Ramanujan-type supercongruence conjectures due to Van Hamme from 1997. The proof utilizes classical... 
Wilf–Zeilberger pair | Ramanujan | Supercongruence | Wilf-Zeilberger pair | MATHEMATICS | MATHEMATICS, APPLIED | FORMULAS
Journal Article
Acta Universitatis Sapientiae, Mathematica, ISSN 1844-6094, 08/2018, Volume 10, Issue 1, pp. 125 - 133
In the paper, the authors find the sum of the Lah numbers and make sure that the Kummer confluent hypergeometric function (n+ 1; 2; z) has only n− 1real and... 
Lah number | zero | Kummer confluent hypergeometric function | sum | Secondary 05A10, 05A19, 11B65, 11B99, 30C15, 33C15, 65B10 | Primary 11B83 | 65B10 | 33C15 | Secondary 05A10 | 11B65 | 05A19 | 11B99 | 30C15
Journal Article
Experimental Mathematics, ISSN 1058-6458, 10/2018, Volume 27, Issue 4, pp. 437 - 443
Some class of sums which naturally include the sums of powers of integers is considered. A number of conjectures concerning a representation of these sums are... 
sums of powers of integers | Bernoulli numbers | Faulhaber's theorem | 11B65 | 11B68 | MATHEMATICS
Journal Article
Journal of mathematical analysis and applications, ISSN 0022-247X, 2019, Volume 475, Issue 2, pp. 1636 - 1646
There are many instances known when the Fourier coefficients of modular forms are congruent to partial sums of hypergeometric series. In our previous work,... 
Cyclotomic polynomial | Basic hypergeometric function | Ramanujan | (Super)congruence | q-Analogue | Q-ANALOG | 1/PI | MATHEMATICS | MATHEMATICS, APPLIED | RAMANUJAN-TYPE FORMULAS | SUPERCONGRUENCE | CONGRUENCES
Journal Article
Resultate der Mathematik, ISSN 1420-9012, 2019, Volume 75, Issue 1, pp. 1 - 15
We provide several new q-congruences for truncated basic hypergeometric series with the base being an even power of q. Our results mainly concern congruences... 
Primary 33D15 | Andrews’ transformation | supercongruences | q -congruences | cyclotomic polynomial | 11B65 | Mathematics, general | Mathematics | Basic hypergeometric series | Secondary 11A07 | q-congruences
Journal Article
Bulletin of the London Mathematical Society, ISSN 0024-6093, 10/2017, Volume 49, Issue 5, pp. 770 - 783
By considering a limiting case of a Kronecker‐type identity, we obtain an identity found by both Andrews and Crandall. We then use the Andrews–Crandall... 
11B65 (primary) | 11E25 | 05A15 (secondary) | FORMS | MATHEMATICS | YZ PLUS ZX | Mathematics - Number Theory
Journal Article
Journal of the Mathematical Society of Japan, ISSN 0025-5645, 2014, Volume 66, Issue 3, pp. 927 - 949
Let v(d)((s)) denote the set of coefficient vectors of contractive polynomials of degree d with 2s non-real zeros. We prove that v(d)((s)) can be computed by a... 
Polynomials with bounded roots | Selberg integral | MATHEMATICS | polynomials with bounded roots
Journal Article
The Ramanujan journal, ISSN 1572-9303, 2018, Volume 49, Issue 3, pp. 531 - 544
Motivated by Zudilin’s work, we give q-analogues of the Ramanujan-type supercongruences (E.2) and (F.2) of Van Hamme. Our proof utilizes the q-WZ method and... 
Cyclotomic polynomials | Ramanujan | 05A30 | Functions of a Complex Variable | Secondary 05A10 | Supercongruences | Field Theory and Polynomials | Primary 11B65 | Mathematics | q -Analogues | q -WZ pair | Fourier Analysis | Number Theory | Combinatorics | q-WZ pair | q-Analogues | MATHEMATICS | CONGRUENCES | Employee motivation
Journal Article
European Journal of Combinatorics, ISSN 0195-6698, 11/2016, Volume 58, pp. 247 - 266
Rook theory has been investigated by many people since its introduction by Kaplansky and Riordan in 1946. Goldman, Joichi, and White in 1975 showed that the... 
MATHEMATICS | NUMBERS | FROBENIUS | Mathematics - Combinatorics
Journal Article
Mathematica Slovaca, ISSN 0139-9918, 06/2018, Volume 68, Issue 3, pp. 501 - 512
Recently Marques and Trojovsky [On some new identities for the Fibonomial coefficients, Math. Slovaca 64 (2014), 809–818] presented interesting two sum... 
Fibonomial coefficients | Gaussian | binomial coefficients | sum identities | Primary 11B65, 05A10, 11B37 | Gaussian q-binomial coefficients
Journal Article
Mathematika, ISSN 0025-5793, 01/2015, Volume 61, Issue 1, pp. 63 - 71
In this paper we present a new family of identities for multiple harmonic sums which generalize a recent result of Hessami Pilehrood et al  [Trans. Amer. Math.... 
11B65 | 11M32 (primary) | MATHEMATICS | MATHEMATICS, APPLIED | MOTIVES | Mathematics - Number Theory
Journal Article
Mathematische Annalen, ISSN 0025-5831, 2/2017, Volume 367, Issue 1, pp. 373 - 395
Denote by p(n) the number of partitions of n and by N(a, M; n) the number of partitions of n with rank congruent to a modulo M. We find and prove a general... 
11B65 | Mathematics, general | 11F27 | Mathematics | 11P84 | 11F11 | FORMS | MATHEMATICS | SYMMETRIES | SERIES | OVERPARTITIONS | PARTITIONS | MOCK THETA-FUNCTIONS | Polyimides | Mathematics - Number Theory
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 04/2017, Volume 448, Issue 2, pp. 1061 - 1078
In this paper, we confirm several conjectured congruences of Sun concerning the divisibility of binomial sums. For example, with help of a quadratic... 
Congruence | Pell number | Central binomial coefficient | LEGENDRE POLYNOMIALS | MATHEMATICS | MATHEMATICS, APPLIED | RODRIGUEZ-VILLEGAS | ANALOGS | HYPERGEOMETRIC-SERIES | CONGRUENCES | CONJECTURE
Journal Article
Journal of difference equations and applications, ISSN 1563-5120, 2018, Volume 24, Issue 9, pp. 1473 - 1487
We prove two conjectures on sums of products of Catalan triangle numbers, which were originally conjectured by Miana et al. [Discrete Math. 340 (2017),... 
cyclotomic polynomial | Zeilberger's algorithm | Catalan numbers | Catalan triangle | q-Chu-Vandermonde summation | 05A30 | 05A10 | 11B65 | MATHEMATICS, APPLIED | IDENTITIES | BINOMIAL COEFFICIENTS | POWER | MOMENTS | SUMS
Journal Article
Compositio mathematica, ISSN 0010-437X, 02/2018, Volume 154, Issue 2, pp. 249 - 274
We provide lower bounds for $p$ -adic valuations of multisums of factorial ratios which satisfy an Apéry-like recurrence relation: these include Apéry, Domb... 
congruences | Apéry numbers | p-Lucas property | constant terms of powers of Laurent polynomials | MATHEMATICS | CONGRUENCE PROPERTIES | 11B65 | COEFFICIENTS | 05A10 (secondary) | 11B50 (primary) | Apery numbers | POWERS | Mathematics | Number Theory
Journal Article
Journal of inequalities and applications, ISSN 1029-242X, 2018, Volume 2018, Issue 1, pp. 1 - 14
Recently, Mortenson (Proc. Edinb. Math. Soc. 4:1–13, 2015) explored the bilateral series in terms of Appell–Lerch sums for the universal mock theta function... 
11F03 | Appell–Lerch sums | 11F27 | Bilateral series | Analysis | 11B65 | Mathematics, general | Mathematics | Applications of Mathematics | Mock theta functions | MATHEMATICS | MATHEMATICS, APPLIED | Appell-Lerch sums | Sums | Research
Journal Article
Duke Mathematical Journal, ISSN 0012-7094, 2001, Volume 108, Issue 3, pp. 395 - 419
As usual, define Dedekind's eta-function eta (z) by the infinite product [GRAPHICS] In a recent paper D. Zagier proved that (note: empty products equal 1... 
MATHEMATICS | 11B65 | 11F20
Journal Article
Journal of Inequalities and Applications, ISSN 1025-5834, 12/2018, Volume 2018, Issue 1, pp. 1 - 10
It is known that the concept of ratio monotonicity is closely related to log-convexity and log-concavity. In this paper, by exploring the log-behavior... 
log-concavity | interlacing method | Analysis | 05A10 | 05A20 | 11B65 | Mathematics, general | Mathematics | log-convexity | Applications of Mathematics | ratio monotonicity | 11B37 | MATHEMATICS | MATHEMATICS, APPLIED | COMBINATORIAL SEQUENCES | Research
Journal Article
Journal of Inequalities and Applications, ISSN 1025-5834, 12/2019, Volume 2019, Issue 1, pp. 1 - 11
Journal Article
Arabian journal of mathematics, ISSN 2193-5343, 06/2018, Volume 7, Issue 2, pp. 101 - 112
We present three new sets of weighted partial sums of the Gaussian q-binomial coefficients. To prove the claimed results, we will use q-analysis, Rothe’s... 
Binomial coefficients | Sums | 05A30 | 11B65
Journal Article
No results were found for your search.

Cannot display more than 1000 results, please narrow the terms of your search.