• Title, Summary, Keyword: recurrence relation

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SOME RECURRENCE RELATIONS OF MULTIPLE ORTHOGONAL POLYNOMIALS

  • Lee, Dong-Won
    • Journal of the Korean Mathematical Society
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    • v.42 no.4
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    • pp.673-693
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    • 2005
  • In this paper, we first find a necessary and sufficient condition for the existence of multiple orthogonal polynomials by the moments of a pair of measures $(d{\mu},\;dv)$ and then give representations for multiple orthogonal polynomials. We also prove four term recurrence relations for multiple orthogonal polynomials of type II and several interesting relations for multiple orthogonal polynomials are given. A generalized recurrence relation for multiple orthogonal polynomials of type I is found and then four term recurrence relations are obtained as a special case.

Recurrence Relation and Characterization of The Rayleigh Distribution Using Order Statistics

  • Lee, In-Suk;Kim, Sang-Moon
    • Journal of the Korean Data and Information Science Society
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    • v.10 no.2
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    • pp.299-311
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    • 1999
  • In this paper the single and product moments of order statistics of the doubly truncated Rayleigh distribution are studied. Some recurrence relations of order statistics are derived. Using order statistics, also characterization of the Rayleigh distribution are derived.

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A RECURRENCE RELATION FOR THE JONES POLYNOMIAL

  • Berceanu, Barbu;Nizami, Abdul Rauf
    • Journal of the Korean Mathematical Society
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    • v.51 no.3
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    • pp.443-462
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    • 2014
  • Using a simple recurrence relation, we give a new method to compute the Jones polynomials of closed braids: we find a general expansion formula and a rational generating function for the Jones polynomials. The method is used to estimate the degree of the Jones polynomials for some families of braids and to obtain general qualitative results.

Recurrence Relations in the Transformed Exponential Distributions

  • Choi, Jeen-Kap;Mo, Kap-Jong
    • Journal of the Korean Data and Information Science Society
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    • v.14 no.4
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    • pp.1031-1044
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    • 2003
  • In this paper, we establish some recurrence relations of the moments, product moments, percentage points, and modes of order statistics from the transformed exponential distribution.

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Clinical statistics: five key statistical concepts for clinicians

  • Choi, Yong-Geun
    • Journal of the Korean Association of Oral and Maxillofacial Surgeons
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    • v.39 no.5
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    • pp.203-206
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    • 2013
  • Statistics is the science of data. As the foundation of scientific knowledge, data refers to evidentiary facts from the nature of reality by human action, observation, or experiment. Clinicians should be aware of the conditions of good data to support the validity of clinical modalities in reading scientific articles, one of the resources to revise or update their clinical knowledge and skills. The cause-effect link between clinical modality and outcome is ascertained as pattern statistic. The uniformity of nature guarantees the recurrence of data as the basic scientific evidence. Variation statistics are examined for patterns of recurrence. This provides information on the probability of recurrence of the cause-effect phenomenon. Multiple causal factors of natural phenomenon need a counterproof of absence in terms of the control group. A pattern of relation between a causal factor and an effect becomes recognizable, and thus, should be estimated as relation statistic. The type and meaning of each relation statistic should be well-understood. A study regarding a sample from the population of wide variations require clinicians to be aware of error statistics due to random chance. Incomplete human sense, coarse measurement instrument, and preconceived idea as a hypothesis that tends to bias the research, which gives rise to the necessity of keen critical independent mind with regard to the reported data.

SOME PROPERTIES OF GENERALIZED HYPERGEOMETRIC FUNCTION

  • Rao, Snehal B.;Patel, Amit D.;Prajapati, Jyotindra C.;Shukla, Ajay K.
    • Communications of the Korean Mathematical Society
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    • v.28 no.2
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    • pp.303-317
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    • 2013
  • In present paper, we obtain functions $R_t(c,{\nu},a,b)$ and $R_t(c,-{\mu},a,b)$ by using generalized hypergeometric function. A recurrence relation, integral representation of the generalized hypergeometric function $_2R_1(a,b;c;{\tau};z)$ and some special cases have also been discussed.