R e p r o d u c e d with p e r m issio n o f th e co p y rig h t o w n e r. F u rth er rep ro d u... more R e p r o d u c e d with p e r m issio n o f th e co p y rig h t o w n e r. F u rth er rep ro d u ctio n p roh ib ited w ith o u t p e r m issio n .
In this paper we calculate some remarkable cubic and quartic series involving the tail of ln2. We... more In this paper we calculate some remarkable cubic and quartic series involving the tail of ln2. We also evaluate several linear and quadratic series with the tail of ln2.
where a denotes the greatest integer less than or equal to a. 1850. Proposed by Richard Stephens,... more where a denotes the greatest integer less than or equal to a. 1850. Proposed by Richard Stephens, Department of Mathematics, Columbus State University, Columbus, GA. Let τ be a topology on a finite set X . Define a topology on X to be regular if for any nonempty closed E ⊆ X and x ∈ X \ E , there exist disjoint open sets U and V in τ such that E ⊆ V and x ∈ U . Prove or disprove that the topological space (X, τ ) is regular if and only if τ has a base B which is a partition of X .
The paper is about evaluating in closed form the following classes of series involving the produc... more The paper is about evaluating in closed form the following classes of series involving the product of the n th harmonic number and the polygamma functions
In this paper we give a new technique for the calculation of the matrix exponential function e as... more In this paper we give a new technique for the calculation of the matrix exponential function e as well as the matrix trigonometric functions sinA and cosA, where A ∈ M2 (C). We also determine the real logarithm of the matrix xI2, when x ∈ R∗, as well as the real logarithm of scalar multiple of rotation and reflection matrices. The real logarithm of a real circulant matrix and a symmetric matrix are also determined.
If f is a nonnegative continuous function on [0, 1] we investigate the problem when is ... equal ... more If f is a nonnegative continuous function on [0, 1] we investigate the problem when is ... equal to the supremum norm of f. This problem is motivated by a problem in classical analysis which states that if f is a continuous function on [a, b] then the following equality holds
The paper gives a unified treatment of the summation of certain iterated series of the form ∑∞ ∑ ... more The paper gives a unified treatment of the summation of certain iterated series of the form ∑∞ ∑ ∞ n=1 m=1 an+m, where (an)n∈N is a sequence of real numbers. We prove that, under certain conditions, the double iterated series equals the difference of two single series. 1
In this paper we give a new proof of the following remarkable series formula ∞ ∑ n=1 ( Hn n )2 = ... more In this paper we give a new proof of the following remarkable series formula ∞ ∑ n=1 ( Hn n )2 = 17 4 ζ(4), where Hn = 1+ 1 2 + · · ·+ 1 n denotes the nth harmonic number. The proof is based on evaluating a special harmonic series by two different methods.
R e p r o d u c e d with p e r m issio n o f th e co p y rig h t o w n e r. F u rth er rep ro d u... more R e p r o d u c e d with p e r m issio n o f th e co p y rig h t o w n e r. F u rth er rep ro d u ctio n p roh ib ited w ith o u t p e r m issio n .
In this paper we calculate some remarkable cubic and quartic series involving the tail of ln2. We... more In this paper we calculate some remarkable cubic and quartic series involving the tail of ln2. We also evaluate several linear and quadratic series with the tail of ln2.
where a denotes the greatest integer less than or equal to a. 1850. Proposed by Richard Stephens,... more where a denotes the greatest integer less than or equal to a. 1850. Proposed by Richard Stephens, Department of Mathematics, Columbus State University, Columbus, GA. Let τ be a topology on a finite set X . Define a topology on X to be regular if for any nonempty closed E ⊆ X and x ∈ X \ E , there exist disjoint open sets U and V in τ such that E ⊆ V and x ∈ U . Prove or disprove that the topological space (X, τ ) is regular if and only if τ has a base B which is a partition of X .
The paper is about evaluating in closed form the following classes of series involving the produc... more The paper is about evaluating in closed form the following classes of series involving the product of the n th harmonic number and the polygamma functions
In this paper we give a new technique for the calculation of the matrix exponential function e as... more In this paper we give a new technique for the calculation of the matrix exponential function e as well as the matrix trigonometric functions sinA and cosA, where A ∈ M2 (C). We also determine the real logarithm of the matrix xI2, when x ∈ R∗, as well as the real logarithm of scalar multiple of rotation and reflection matrices. The real logarithm of a real circulant matrix and a symmetric matrix are also determined.
If f is a nonnegative continuous function on [0, 1] we investigate the problem when is ... equal ... more If f is a nonnegative continuous function on [0, 1] we investigate the problem when is ... equal to the supremum norm of f. This problem is motivated by a problem in classical analysis which states that if f is a continuous function on [a, b] then the following equality holds
The paper gives a unified treatment of the summation of certain iterated series of the form ∑∞ ∑ ... more The paper gives a unified treatment of the summation of certain iterated series of the form ∑∞ ∑ ∞ n=1 m=1 an+m, where (an)n∈N is a sequence of real numbers. We prove that, under certain conditions, the double iterated series equals the difference of two single series. 1
In this paper we give a new proof of the following remarkable series formula ∞ ∑ n=1 ( Hn n )2 = ... more In this paper we give a new proof of the following remarkable series formula ∞ ∑ n=1 ( Hn n )2 = 17 4 ζ(4), where Hn = 1+ 1 2 + · · ·+ 1 n denotes the nth harmonic number. The proof is based on evaluating a special harmonic series by two different methods.
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Papers by Ovidiu Furdui