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Volume 8 Issue 8
August-2021
eISSN: 2349-5162

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JETIR2108647


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319972

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f358-f362

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Title

SOME RESULTS ON METHOD OF GENERATING FUNCTION

Abstract

The use of generating functions with many applications in number theory and combinatory is a very important and powerful technique. In this section we will describe this technique in more detail. By the manipulation and interpretation of series and product identities, the generating function is an important contribution in proving division functions. The main function of the generating function is to determine the coefficient of y or to get upper or lower limit of coefficient of y. One can also use the generating function to come on asymmetric value of coefficient of y (if possible). A good example of this application is to “show that, P(i) < e3√i for all by (Cohen, 1978). Definition (Partition) In Z+ , ∑_(λ=1)^(λ=r)▒a_λ =a_1+ a_2+⋯+ a_r= i where a_λ are parts or summands of that partition. For understanding we can take four which can be written as a 1+1+1+1, 1+1+2, 1+3, 2+2 and 4, hence P (4)=five. Definition . Let f_i (i) count partitions into the integers 1,2,...,k, with repetitions allowed. Definition. Let f_O (i) count partitions (odd integers) of i such that repetitions allowed. Definition . Let f_d (i) count partitions distinct parts Definition . Let f_t (i) count partitions distinct powers of 2, (i.e., into 1,2,4,8,...). Our discussion above showed (Generating function) f_k (i) = 1/([( 1- y)(l -y2)(l -y3)]). From Theorem we find immediately

Key Words

Generating Function, Partition, identities , Division.

Cite This Article

"SOME RESULTS ON METHOD OF GENERATING FUNCTION", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.8, Issue 8, page no.f358-f362, August-2021, Available :http://www.jetir.org/papers/JETIR2108647.pdf

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2349-5162 | Impact Factor 7.95 Calculate by Google Scholar

An International Scholarly Open Access Journal, Peer-Reviewed, Refereed Journal Impact Factor 7.95 Calculate by Google Scholar and Semantic Scholar | AI-Powered Research Tool, Multidisciplinary, Monthly, Multilanguage Journal Indexing in All Major Database & Metadata, Citation Generator

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"SOME RESULTS ON METHOD OF GENERATING FUNCTION", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.8, Issue 8, page no. ppf358-f362, August-2021, Available at : http://www.jetir.org/papers/JETIR2108647.pdf

Publication Details

Published Paper ID: JETIR2108647
Registration ID: 319972
Published In: Volume 8 | Issue 8 | Year August-2021
DOI (Digital Object Identifier):
Page No: f358-f362
Country: -, -, India .
Area: Engineering
ISSN Number: 2349-5162
Publisher: IJ Publication


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