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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 발행연도
- 2010.1
- 수록면
- 177 - 193 (17page)
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Working with the various special functions of mathematical physics and applied mathematics we often encounter inverse relations of the type Fn(x)= Σk=0nAknGk(x) and Gn(x)=Σk=0nBknFk(x)where $n=0,1,2,… Here Fn(x), Gn(x) denote special polynomial functions, and Akn , Bkn denote coefficients found by use of the orthogonal properties of Fn(x) and Gn(x), or by skillful series manipulations. Typically Gn(x)=xn and Fn(x)=Pn(x), the n-th Legendre polynomial. We give a collection of inverse series pairs of the type Fn(x)= Σk=0nAknG(k) if and if G(n)=Σk=0nBknF(k),each pair being based on some reasonably well-known special function. We also state and prove an interesting generalization of a theorem of Rainville in this form.
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참고문헌 (12)
참고문헌 신청
E. D. Rainville / 1971 / Special Functions / Chelsea Publs.
G. P. Egorychev / 1984 / Integral Representation and the Computation of Combinatorial Sums / Translations of Mathematical Monographs 59
H. W. Gould / 1962 / Operational formulas connected with two generaliza-tions of Hermite polynomials / Duke Math. J. 29 : 51 ~ 63
H. W. Gould / 1965 / Inverse series relations and other expansions involving Humbert poly-nomials / Duke Math. J. 32 : 697 ~ 711
H. W. Gould / 1972 / Combinatorial Identities
G. P. Egorychev / 1984 / Integral Representation and the Computation of Combinatorial Sums / Translations of Mathematical Monographs 59
H. W. Gould / 1962 / Operational formulas connected with two generaliza-tions of Hermite polynomials / Duke Math. J. 29 : 51 ~ 63
H. W. Gould / 1965 / Inverse series relations and other expansions involving Humbert poly-nomials / Duke Math. J. 32 : 697 ~ 711
H. W. Gould / 1972 / Combinatorial Identities
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