http://chineseinput.net/에서 pinyin(병음)방식으로 중국어를 변환할 수 있습니다.
변환된 중국어를 복사하여 사용하시면 됩니다.
Choi, Junesang,Shine, Raj S.N.,Rathie, Arjun K. The Youngnam Mathematical Society 2015 East Asian mathematical journal Vol.31 No.1
We use some known contiguous function relations for $_2F_1$ to show how simply the following three recurrence relations for Jacobi polynomials $P_n^{({\alpha},{\beta)}(x)$: (i) $({\alpha}+{\beta}+n)P_n^{({\alpha},{\beta})}(x)=({\beta}+n)P_n^{({\alpha},{\beta}-1)}(x)+({\alpha}+n)P_n^{({\alpha}-1,{\beta})}(x);$ (ii) $2P_n^{({\alpha},{\beta})}(x)=(1+x)P_n^{({\alpha},{\beta}+1)}(x)+(1-x)P_n^{({\alpha}+1,{\beta})}(x);$ (iii) $P_{n-1}^{({\alpha},{\beta})}(x)=P_n^{({\alpha},{\beta}-1)}(x)+P_n^{({\alpha}-1,{\beta})}(x)$ can be established.
A FAMILY OF NEW RECURRENCE RELATIONS FOR THE JACOBI POLYNOMIALS P_n ^ (α, β) (x)
Shine Raj S.N.,최준상,Arjun K. Rathie 호남수학회 2018 호남수학학술지 Vol.40 No.1
The objective of this paper is to present 87 recurrencerelations for the Jacobi polynomials P( ; )n (x). The results presentedhere most of which are presumably new are obtained withthe help of Gauss's fteen contiguous function relations and someother identities recently recorded in the literature.
A FAMILY OF NEW RECURRENCE RELATIONS FOR THE JACOBI POLYNOMIALS P<sub>n</sub><sup>(α,β)</sup> (x)
( Shine Raj S. N. ),( Junesang Choi ),( Arjun K. Rathie ) 호남수학회 2018 호남수학학술지 Vol.40 No.1
The objective of this paper is to present 87 recurrence relations for the Jacobi polynomialsP<sub>n</sub><sup>(α,β)</sup> (x). The results pre-sented here most of which are presumably new are obtained with the help of Gauss's fifteen contiguous function relations and some other identities recently recorded in the literature.
Some recurrence relations for the Jacobi polynomials Pn(α,β)(x)
최준상,Shine Raj S.N.,A. K. Rathie 영남수학회 2015 East Asian mathematical journal Vol.31 No.1
We use some known contiguous function relations for 2F1 toshow how simply the following three recurrence relations for Jacobi polynomials Pn(α,β)(x): (i) (α+β+n)Pn(α,β)(x)=(β+n)Pn(α,β-1)(x)+(α+n)Pn(α-1,β)(x); (ii) 2Pn(α,β)(x)=(1+x)Pn((α,β+1)(x)+(1-x)Pn((α+1,β)}(x); (iii)Pn-1(α,β)(x)=Pn(α,β-1)(x)+Pn(α-1,β)(x) can be established.