| Summary: | 碩士 === 中原大學 === 應用數學研究所 === 95 === Abstract
Recently we apply fractional calculus theory in Hypergeometric
polynomial, had discussed the D􀭸μ􀵛z􀮛􀬿􀬵􀭮F􀭯􀵣􁈺α􀭮􁈻;􁈺β􀭯􁈻;ωz􀵧􀵟 or D􀭸μ􁈼􀭮F􀭯􁈽
for p and q in the special case etc. In 2005 the academic journal can be
found, Shy-Der Lin, Yi-Shan Chao. and H. M. Srivastava have been
discussed about the Hypergeometric polynomialN􀬾LFM、N􀬾LF􀬴、NFM、
NF􀬴(i.e. S􀭬L,,NM、P􀭬L,N、QM􀭬,N、 R􀭬,N), which computing by double-integral
and triple-integral. Now the main objective of this paper is based on the
fractional calculus theory and Shy-Der Lin’s discussion. We use the
techniques of fractional derivative in series of the Hypergeometric polynomialsN􀬾LFM、N􀵅LF0、NFM、NF􀬴 in order to observe the
transformation, computing and the relation with original polynomail.
By the discussion, we find out that when the derivative order is a
positive integer or a positive rational number, the results are very different.
In this research we decide to focus on the discussion of positive integer here,
and glance at "the derivative order is a positive rational number" in the final
chapter only.
Keyword：Fractional Calculus, Hypergeometric polynomial,
Special function
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