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Half-Integer Values of the Sums of Harmonic Numbers of Order Two
被引:0
作者
:
Sofo, A.
论文数:
0
引用数:
0
h-index:
0
机构:
Victoria Univ, Melbourne, Vic, Australia
Victoria Univ, Melbourne, Vic, Australia
Sofo, A.
[
1
]
机构
:
[1]
Victoria Univ, Melbourne, Vic, Australia
来源
:
UKRAINIAN MATHEMATICAL JOURNAL
|
2017年
/ 68卷
/ 10期
关键词
:
IDENTITIES;
FORMULA;
D O I
:
10.1007/s11253-017-1316-8
中图分类号
:
O29 [应用数学];
学科分类号
:
070104 ;
摘要
:
Half-integer values of the sums of harmonic numbers and reciprocal binomial coefficients are investigated. Closed-form representations and integral expressions are developed for the infinite series.
引用
收藏
页码:1637 / 1650
页数:14
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The evaluation of character Euler double sums
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Dalhousie Univ, Fac Comp Sci, Halifax, NS B3H 3J5, Canada
Kings Coll London, Wheatstone Phys Lab, London WC2R 2LS, England
Borwein, J. M.
Zucker, I. J.
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引用数:
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h-index:
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Kings Coll London, Wheatstone Phys Lab, London WC2R 2LS, England
Kings Coll London, Wheatstone Phys Lab, London WC2R 2LS, England
Zucker, I. J.
Boersma, J.
论文数:
0
引用数:
0
h-index:
0
机构:
Eindhoven Univ Technol, Dept Math & Comp Sci, NL-5600 MB Eindhoven, Netherlands
Kings Coll London, Wheatstone Phys Lab, London WC2R 2LS, England
Boersma, J.
[J].
RAMANUJAN JOURNAL,
2008,
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(03)
: 377
-
405
[3]
Values of the polygamma functions at rational arguments (vol 40, pg 15019, 2007)
Choi, J.
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0
引用数:
0
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0
Choi, J.
Cvijovic, D.
论文数:
0
引用数:
0
h-index:
0
Cvijovic, D.
[J].
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL,
2010,
43
(23)
[4]
Choi J., 2013, J INEQUAL APPL, V49
[5]
Some summation formulas involving harmonic numbers and generalized harmonic numbers
Choi, Junesang
论文数:
0
引用数:
0
h-index:
0
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Dongguk Univ, Dept Math, Gyeongju 780714, South Korea
Univ Victoria, Dept Math & Stat, Victoria, BC V8W 3R4, Canada
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Srivastava, H. M.
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Univ Victoria, Dept Math & Stat, Victoria, BC V8W 3R4, Canada
Univ Victoria, Dept Math & Stat, Victoria, BC V8W 3R4, Canada
Srivastava, H. M.
[J].
MATHEMATICAL AND COMPUTER MODELLING,
2011,
54
(9-10)
: 2220
-
2234
[6]
A Simple Computation of ζ (2k)
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0
引用数:
0
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Univ La Rioja, Dept Matemat & Comp, Logrono 26004, Spain
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Navas, Luis M.
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引用数:
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h-index:
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机构:
Univ Salamanca, Dept Matemat, E-37008 Salamanca, Spain
Univ La Rioja, Dept Matemat & Comp, Logrono 26004, Spain
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Ruiz, Francisco J.
论文数:
0
引用数:
0
h-index:
0
机构:
Univ Zaragoza, Dept Matemat, E-50009 Zaragoza, Spain
Univ La Rioja, Dept Matemat & Comp, Logrono 26004, Spain
Ruiz, Francisco J.
Varona, Juan L.
论文数:
0
引用数:
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h-index:
0
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Univ La Rioja, Dept Matemat & Comp, Logrono 26004, Spain
Univ La Rioja, Dept Matemat & Comp, Logrono 26004, Spain
Varona, Juan L.
[J].
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2015,
122
(05)
: 444
-
451
[7]
Euler sums and contour integral representations
Flajolet, P
论文数:
0
引用数:
0
h-index:
0
机构:
Inst Natl Rech Informat & Automat, Algorithms PROJECT, F-78153 Le Chesnay, France
Inst Natl Rech Informat & Automat, Algorithms PROJECT, F-78153 Le Chesnay, France
Flajolet, P
Salvy, B
论文数:
0
引用数:
0
h-index:
0
机构:
Inst Natl Rech Informat & Automat, Algorithms PROJECT, F-78153 Le Chesnay, France
Inst Natl Rech Informat & Automat, Algorithms PROJECT, F-78153 Le Chesnay, France
Salvy, B
[J].
EXPERIMENTAL MATHEMATICS,
1998,
7
(01)
: 15
-
35
[8]
The polygamma function psi((k))(X) for x=1/4 and x=3/4
Kolbig, KS
论文数:
0
引用数:
0
h-index:
0
机构:
CERN, COMP & NETWORKS DIV, CH-1211 GENEVA 23, SWITZERLAND
CERN, COMP & NETWORKS DIV, CH-1211 GENEVA 23, SWITZERLAND
Kolbig, KS
[J].
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS,
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(01)
: 43
-
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[9]
Harmonic number identities via hypergeometric series and Bell polynomials
Liu, Hongmei
论文数:
0
引用数:
0
h-index:
0
机构:
Dalian Nationalities Univ, Sch Sci, Dalian 116600, Peoples R China
Zhejiang Sci Tech Univ, Sch Sci, Hangzhou 310018, Zhejiang, Peoples R China
Liu, Hongmei
Wang, Weiping
论文数:
0
引用数:
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h-index:
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机构:
Zhejiang Sci Tech Univ, Sch Sci, Hangzhou 310018, Zhejiang, Peoples R China
Zhejiang Sci Tech Univ, Sch Sci, Hangzhou 310018, Zhejiang, Peoples R China
Wang, Weiping
[J].
INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS,
2012,
23
(01)
: 49
-
68
[10]
A FORMULA OF RAMANUJAN,S.
SITARAMACHANDRARAO, R
论文数:
0
引用数:
0
h-index:
0
机构:
UNIV TOLEDO, DEPT MATH, TOLEDO, OH 43606 USA
UNIV TOLEDO, DEPT MATH, TOLEDO, OH 43606 USA
SITARAMACHANDRARAO, R
[J].
JOURNAL OF NUMBER THEORY,
1987,
25
(01)
: 1
-
19
←
1
2
3
→
共 23 条
[1]
[Anonymous], COMPUTATIONAL TECHNI
[2]
The evaluation of character Euler double sums
Borwein, J. M.
论文数:
0
引用数:
0
h-index:
0
机构:
Dalhousie Univ, Fac Comp Sci, Halifax, NS B3H 3J5, Canada
Kings Coll London, Wheatstone Phys Lab, London WC2R 2LS, England
Borwein, J. M.
Zucker, I. J.
论文数:
0
引用数:
0
h-index:
0
机构:
Kings Coll London, Wheatstone Phys Lab, London WC2R 2LS, England
Kings Coll London, Wheatstone Phys Lab, London WC2R 2LS, England
Zucker, I. J.
Boersma, J.
论文数:
0
引用数:
0
h-index:
0
机构:
Eindhoven Univ Technol, Dept Math & Comp Sci, NL-5600 MB Eindhoven, Netherlands
Kings Coll London, Wheatstone Phys Lab, London WC2R 2LS, England
Boersma, J.
[J].
RAMANUJAN JOURNAL,
2008,
15
(03)
: 377
-
405
[3]
Values of the polygamma functions at rational arguments (vol 40, pg 15019, 2007)
Choi, J.
论文数:
0
引用数:
0
h-index:
0
Choi, J.
Cvijovic, D.
论文数:
0
引用数:
0
h-index:
0
Cvijovic, D.
[J].
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL,
2010,
43
(23)
[4]
Choi J., 2013, J INEQUAL APPL, V49
[5]
Some summation formulas involving harmonic numbers and generalized harmonic numbers
Choi, Junesang
论文数:
0
引用数:
0
h-index:
0
机构:
Dongguk Univ, Dept Math, Gyeongju 780714, South Korea
Univ Victoria, Dept Math & Stat, Victoria, BC V8W 3R4, Canada
Choi, Junesang
Srivastava, H. M.
论文数:
0
引用数:
0
h-index:
0
机构:
Univ Victoria, Dept Math & Stat, Victoria, BC V8W 3R4, Canada
Univ Victoria, Dept Math & Stat, Victoria, BC V8W 3R4, Canada
Srivastava, H. M.
[J].
MATHEMATICAL AND COMPUTER MODELLING,
2011,
54
(9-10)
: 2220
-
2234
[6]
A Simple Computation of ζ (2k)
Ciaurri, Oscar
论文数:
0
引用数:
0
h-index:
0
机构:
Univ La Rioja, Dept Matemat & Comp, Logrono 26004, Spain
Univ La Rioja, Dept Matemat & Comp, Logrono 26004, Spain
Ciaurri, Oscar
Navas, Luis M.
论文数:
0
引用数:
0
h-index:
0
机构:
Univ Salamanca, Dept Matemat, E-37008 Salamanca, Spain
Univ La Rioja, Dept Matemat & Comp, Logrono 26004, Spain
Navas, Luis M.
Ruiz, Francisco J.
论文数:
0
引用数:
0
h-index:
0
机构:
Univ Zaragoza, Dept Matemat, E-50009 Zaragoza, Spain
Univ La Rioja, Dept Matemat & Comp, Logrono 26004, Spain
Ruiz, Francisco J.
Varona, Juan L.
论文数:
0
引用数:
0
h-index:
0
机构:
Univ La Rioja, Dept Matemat & Comp, Logrono 26004, Spain
Univ La Rioja, Dept Matemat & Comp, Logrono 26004, Spain
Varona, Juan L.
[J].
AMERICAN MATHEMATICAL MONTHLY,
2015,
122
(05)
: 444
-
451
[7]
Euler sums and contour integral representations
Flajolet, P
论文数:
0
引用数:
0
h-index:
0
机构:
Inst Natl Rech Informat & Automat, Algorithms PROJECT, F-78153 Le Chesnay, France
Inst Natl Rech Informat & Automat, Algorithms PROJECT, F-78153 Le Chesnay, France
Flajolet, P
Salvy, B
论文数:
0
引用数:
0
h-index:
0
机构:
Inst Natl Rech Informat & Automat, Algorithms PROJECT, F-78153 Le Chesnay, France
Inst Natl Rech Informat & Automat, Algorithms PROJECT, F-78153 Le Chesnay, France
Salvy, B
[J].
EXPERIMENTAL MATHEMATICS,
1998,
7
(01)
: 15
-
35
[8]
The polygamma function psi((k))(X) for x=1/4 and x=3/4
Kolbig, KS
论文数:
0
引用数:
0
h-index:
0
机构:
CERN, COMP & NETWORKS DIV, CH-1211 GENEVA 23, SWITZERLAND
CERN, COMP & NETWORKS DIV, CH-1211 GENEVA 23, SWITZERLAND
Kolbig, KS
[J].
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS,
1996,
75
(01)
: 43
-
46
[9]
Harmonic number identities via hypergeometric series and Bell polynomials
Liu, Hongmei
论文数:
0
引用数:
0
h-index:
0
机构:
Dalian Nationalities Univ, Sch Sci, Dalian 116600, Peoples R China
Zhejiang Sci Tech Univ, Sch Sci, Hangzhou 310018, Zhejiang, Peoples R China
Liu, Hongmei
Wang, Weiping
论文数:
0
引用数:
0
h-index:
0
机构:
Zhejiang Sci Tech Univ, Sch Sci, Hangzhou 310018, Zhejiang, Peoples R China
Zhejiang Sci Tech Univ, Sch Sci, Hangzhou 310018, Zhejiang, Peoples R China
Wang, Weiping
[J].
INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS,
2012,
23
(01)
: 49
-
68
[10]
A FORMULA OF RAMANUJAN,S.
SITARAMACHANDRARAO, R
论文数:
0
引用数:
0
h-index:
0
机构:
UNIV TOLEDO, DEPT MATH, TOLEDO, OH 43606 USA
UNIV TOLEDO, DEPT MATH, TOLEDO, OH 43606 USA
SITARAMACHANDRARAO, R
[J].
JOURNAL OF NUMBER THEORY,
1987,
25
(01)
: 1
-
19
←
1
2
3
→