Class information for:
Level 1: MULTIPLE ZETA VALUES//HURWITZ ZETA FUNCTION//EULER SUMS

Basic class information
Class id #P Avg. number of
references		 Database coverage
of references
12370 911 17.3 39%


Bar chart of Publication_year

Last years might be incomplete

Hierarchy of classes
The table includes all classes above and classes immediately below the current class.


Cluster id Level Cluster label #P
15 4 MATHEMATICS//MATHEMATICS, APPLIED//MATH 719832
404 3       MATHEMATICS//ORTHOGONAL POLYNOMIALS//MATHEMATICS, APPLIED 29787
1244 2             FIBONACCI QUARTERLY//MULTIPLE ZETA VALUES//BERNOULLI NUMBERS 8992
12370 1                   MULTIPLE ZETA VALUES//HURWITZ ZETA FUNCTION//EULER SUMS 911

Terms with highest relevance score


rank Term termType Chi square Shr. of publ. in
class containing
term		 Class's shr. of
term's tot. occurrences		 #P with
term in
class
1 MULTIPLE ZETA VALUES authKW 3489930 13% 88% 119
2 HURWITZ ZETA FUNCTION authKW 1103925 8% 43% 77
3 EULER SUMS authKW 1076265 4% 94% 34
4 HARMONIC NUMBERS authKW 879852 6% 50% 52
5 RIEMANN ZETA FUNCTION authKW 710451 12% 20% 107
6 GENERALIZED HARMONIC NUMBERS authKW 437954 2% 93% 14
7 MULTIPLE ZETA STAR VALUES authKW 437954 2% 93% 14
8 STIELTJES CONSTANTS authKW 373049 2% 70% 16
9 SUM FORMULA authKW 364957 2% 78% 14
10 POLYGAMMA FUNCTIONS authKW 323742 4% 30% 32

Web of Science journal categories


Rank Term Chi square Shr. of publ. in
class containing
term		 Class's shr. of
term's tot. occurrences		 #P with
term in
class
1 Mathematics 33772 82% 0% 747
2 Mathematics, Applied 6069 33% 0% 299
3 Physics, Mathematical 142 4% 0% 38
4 Statistics & Probability 41 2% 0% 20
5 Computer Science, Software Engineering 4 1% 0% 9
6 Computer Science, Theory & Methods -0 1% 0% 6
7 Computer Science, Interdisciplinary Applications -0 1% 0% 5
8 Physics, Particles & Fields -1 1% 0% 6
9 Physics, Nuclear -6 0% 0% 1
10 Mechanics -7 0% 0% 2

Address terms


Rank Term Chi square Shr. of publ. in
class containing
term		 Class's shr. of
term's tot. occurrences		 #P with
term in
class
1 VICTORIA UNIV 83788 1% 50% 5
2 HBEREICH MATH AZ 67034 0% 100% 2
3 ALGEBRA GEOMETRY MATH 33517 0% 100% 1
4 ALGORITHM ARTHMET EXPT A2X 33517 0% 100% 1
5 GLOBAL BIG DATA MATHCHIYODA KU 33517 0% 100% 1
6 GRP FIS TEORIA MATEMAT UNITA TECN 33517 0% 100% 1
7 IST MATEMAT GUIDO CASTELNUOVO 33517 0% 100% 1
8 KAWARABAYASHI LARGE GR H PROJECT INFOR 33517 0% 100% 1
9 MET ESTADJST 33517 0% 100% 1
10 SCI ENGNOKUBO SHINJUKU KU 33517 0% 100% 1

Journals


Rank Term Chi square Shr. of publ. in
class containing
term		 Class's shr. of
term's tot. occurrences		 #P with
term in
class
1 RAMANUJAN JOURNAL 105617 6% 6% 57
2 JOURNAL OF NUMBER THEORY 47923 9% 2% 82
3 INTERNATIONAL JOURNAL OF NUMBER THEORY 26875 3% 3% 30
4 INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS 25790 3% 2% 31
5 COMMUNICATIONS IN NUMBER THEORY AND PHYSICS 20671 1% 6% 10
6 KYUSHU JOURNAL OF MATHEMATICS 15517 1% 4% 11
7 ANALYSIS MATHEMATICA 8426 1% 4% 6
8 ACTA ARITHMETICA 7558 3% 1% 27
9 UTILITAS MATHEMATICA 7300 2% 1% 19
10 APPLICABLE ANALYSIS AND DISCRETE MATHEMATICS 6069 1% 3% 7

Author Key Words


Rank Term Chi square Shr. of publ. in
class containing
term		 Class's shr. of
term's tot. occurrences		 #P with
term in
class		 LCSH search Wikipedia search
1 MULTIPLE ZETA VALUES 3489930 13% 88% 119 Search MULTIPLE+ZETA+VALUES Search MULTIPLE+ZETA+VALUES
2 HURWITZ ZETA FUNCTION 1103925 8% 43% 77 Search HURWITZ+ZETA+FUNCTION Search HURWITZ+ZETA+FUNCTION
3 EULER SUMS 1076265 4% 94% 34 Search EULER+SUMS Search EULER+SUMS
4 HARMONIC NUMBERS 879852 6% 50% 52 Search HARMONIC+NUMBERS Search HARMONIC+NUMBERS
5 RIEMANN ZETA FUNCTION 710451 12% 20% 107 Search RIEMANN+ZETA+FUNCTION Search RIEMANN+ZETA+FUNCTION
6 GENERALIZED HARMONIC NUMBERS 437954 2% 93% 14 Search GENERALIZED+HARMONIC+NUMBERS Search GENERALIZED+HARMONIC+NUMBERS
7 MULTIPLE ZETA STAR VALUES 437954 2% 93% 14 Search MULTIPLE+ZETA+STAR+VALUES Search MULTIPLE+ZETA+STAR+VALUES
8 STIELTJES CONSTANTS 373049 2% 70% 16 Search STIELTJES+CONSTANTS Search STIELTJES+CONSTANTS
9 SUM FORMULA 364957 2% 78% 14 Search SUM+FORMULA Search SUM+FORMULA
10 POLYGAMMA FUNCTIONS 323742 4% 30% 32 Search POLYGAMMA+FUNCTIONS Search POLYGAMMA+FUNCTIONS

Core articles
The table includes core articles in the class. The following variables is taken into account for the relevance score of an article in a cluster c:
(1) Number of references referring to publications in the class.
(2) Share of total number of active references referring to publications in the class.
(3) Age of the article. New articles get higher score than old articles.
(4) Citation rate, normalized to year.


Rank Reference # ref.
in cl.		 Shr. of ref. in
cl.		 Citations
1 WANG, WP , JIA, CZ , (2014) HARMONIC NUMBER IDENTITIES VIA THE NEWTON-ANDREWS METHOD.RAMANUJAN JOURNAL. VOL. 35. ISSUE 2. P. 263 -285 32 89% 8
2 SOFO, A , (2015) QUADRATIC ALTERNATING HARMONIC NUMBER SUMS.JOURNAL OF NUMBER THEORY. VOL. 154. ISSUE . P. 144 -159 20 100% 6
3 SOFO, A , (2016) IDENTITIES FOR ALTERNATING INVERSE SQUARED BINOMIAL AND HARMONIC NUMBER SUMS.MEDITERRANEAN JOURNAL OF MATHEMATICS. VOL. 13. ISSUE 4. P. 1407 -1418 21 100% 0
4 KOMORI, Y , MATSUMOTO, K , TSUMURA, H , (2011) SHUFFLE PRODUCTS FOR MULTIPLE ZETA VALUES AND PARTIAL FRACTION DECOMPOSITIONS OF ZETA-FUNCTIONS OF ROOT SYSTEMS.MATHEMATISCHE ZEITSCHRIFT. VOL. 268. ISSUE 3-4. P. 993-1011 24 92% 3
5 MACHIDE, T , (2012) WEIGHTED SUMS WITH TWO PARAMETERS OF MULTIPLE ZETA VALUES AND THEIR FORMULAS.INTERNATIONAL JOURNAL OF NUMBER THEORY. VOL. 8. ISSUE 8. P. 1903-1921 21 100% 1
6 WEI, CA , WANG, XX , (2016) SUMMATION FORMULAS INVOLVING GENERALIZED HARMONIC NUMBERS.JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS. VOL. 22. ISSUE 10. P. 1554 -1567 23 82% 0
7 ZHAO, JQ , (2016) IDENTITY FAMILIES OF MULTIPLE HARMONIC SUMS AND MULTIPLE ZETA STAR VALUES.JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN. VOL. 68. ISSUE 4. P. 1669 -1694 19 95% 0
8 SOFO, A , (2016) SECOND ORDER ALTERNATING HARMONIC NUMBER SUMS.FILOMAT. VOL. 30. ISSUE 13. P. 3511 -3524 18 100% 0
9 LEI, P , GUO, L , MA, B , (2014) APPLICATIONS OF SHUFFLE PRODUCT TO RESTRICTED DECOMPOSITION FORMULAS FOR MULTIPLE ZETA VALUES.JOURNAL OF NUMBER THEORY. VOL. 144. ISSUE . P. 219 -233 20 91% 3
10 GUO, L , XIE, BY , (2013) EXPLICIT DOUBLE SHUFFLE RELATIONS AND A GENERALIZATION OF EULER'S DECOMPOSITION FORMULA.JOURNAL OF ALGEBRA. VOL. 380. ISSUE . P. 46-77 23 82% 2

Classes with closest relation at Level 1


Rank Class id link
1 12598 GAMMA FUNCTION//PSI FUNCTION//COMPLETELY MONOTONIC FUNCTION
2 9879 GEN EDUC MATH//BERNOULLI POLYNOMIALS//EULER POLYNOMIALS
3 14479 MAHLERS METHOD//IRRATIONALITY MEASURE//ALGEBRAIC INDEPENDENCE
4 29343 SPACE OF ANALYTIC FUNCTIONS//JOINT UNIVERSALITY//PERIODIC HURWITZ ZETA FUNCTION
5 12167 GROBNER SHIRSHOV BASIS//QUASI SYMMETRIC FUNCTIONS//ROTA BAXTER ALGEBRA
6 21228 SYMBOLIC SUMMATION//SYMBOL COMPUTAT//BOROS MOLL POLYNOMIALS
7 16742 STIRLING NUMBERS//R STIRLING NUMBERS//EULER DISTRIBUTION
8 14579 SUPERCONGRUENCES//GAUSSIAN HYPERGEOMETRIC SERIES//BINOMIAL COEFFICIENTS
9 29485 MATHIEU SERIES//DIFFERINTEGRAL EQUATIONS//GENERALIZED LEIBNIZ RULE
10 18028 HYBRID MEAN VALUE//DEDEKIND SUMS//ASYMPTOTIC FORMULA

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