Khrushchev, Sergey

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https://hdl.handle.net/20.500.14411/8378
Name Variants
Khrushchev, S
Khrushchev, S.
Khrushchev, SV
S.,Khrushchev
K.,Sergey
K., Sergey
Sergey, Khrushchev
S., Khrushchev
Khrushchev,S.
Khrushchev, Sergey
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Profesör Doktor
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Mathematics
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Former Staff
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Scholarly Output

18

Articles

6

Views / Downloads

3/0

Supervised MSc Theses

0

Supervised PhD Theses

0

WoS Citation Count

62

Scopus Citation Count

52

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0

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0

WoS Citations per Publication

3.44

Scopus Citations per Publication

2.89

Open Access Source

4

Supervised Theses

0

JournalCount
Journal of Approximation Theory5
7th International Symposium on Orthogonal Polynomials, Special Functions and Applications -- AUG 18-22, 2003 -- Univ Copenhagen, Copenhagen, DENMARK1
Conference on Constructive Functions Tech-04 in honor of Edward B Saff -- NOV 07-09, 2004 -- Georgia Inst Technol, Atlanta, GA1
International Conference on Special Functions, Information Theory and Mathematical Physics -- SEP 17-19, 2007 -- Granada, SPAIN1
Publicacions Matemàtiques1
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Subject: continued fractions

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Now showing 1 - 2 of 2
  • Thumbnail Image
    Conference Object
    Citation - WoS: 2
    Citation - Scopus: 1
    On Euler's differential methods for continued fractions
    (Kent State University, 2006) Khrushchev, Sergey; Mathematics
    A differential method discovered by Euler is justified and applied to give simple proofs to formulas relating important continued fractions with Laplace transforms. They include Stieltjes formulas and some Ramanujan formulas. A representation for the remainder of Leibniz's series as a continued fraction is given. We also recover the original Euler's proof for the continued fraction of hyperbolic cotangent.
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    Review
    Citation - WoS: 5
    Citation - Scopus: 4
    A Recovery of Brouncker's Proof for the Quadrature Continued Fraction
    (Univ Autonoma Barcelona, 2006) Khrushchev, S
    350 years ago in Spring of 1655 Sir William Brouncker on a request by John Wallis obtained a beautiful continued fraction for 4/pi. Brouncker never published his proof. Many sources on the history of Mathematics claim that this proof was lost forever. In this paper we recover the original proof from Wallis' remarks presented in his "Arithmetica Infinitorum". We show that Brouncker's and Wallis' formulas can be extended to MacLaurin's sinusoidal spirals via related Euler's products. We derive Ramanujan's formula from Euler's formula and, by using it, then show that numerators of convergents of Brouncker's continued fractions coincide tip to a rotation with Wilson's orthogonal polynomials corresponding to the parameters a = 0, b = 1/2, c = d = 1/4.