1)  associated Legendre function

1.
Based on the fundamental formula and property of the theory of associated Legendre function,in the paper,the orthogonal properties of different levels and orders of associated Legendre functions p~k_n(x) and p~l_m(x) on the with weight ω(t)=(1-x~2)~(()~(k-l2)) are proved in detail.

2)  Associated Legendre functions of positive integer order

3)  Legendre function

1.
Study of asymptotic relationship between Bessel function and Legendre function by analyzing vibration modes

2.
The solution of Legendre equation has been introduced in the condition of natural limit and the emphasis is put on the inference to the coefficient of the Legendre function.

3.
Based on the fundamental formulae and properties of the theory of Legendre function, the recursive formulae of a group of special fixed integrals that arise in harmonic analysis of gravity gradiometry are deduced in detail; and it is pointed out that these recursive formulae bear certain importance for the theory of harmonic analysis of physical geodesy.

4)  the coefficient of Legendre function

5)  Associated Legendre solution

6)  Associated Legendre functions

 勒让德函数Legendre function   形为（1－x2）y″－2xy′＋n（n＋1）y＝0的方程。   它有级数解：    当n为正偶数时，y1（x）退化成多项式，当n为正奇数时，y2（x）退化成多项式，二者可写成统一的式子：   罗德里克公式： 说明：补充资料仅用于学习参考，请勿用于其它任何用途。 参考词条 ©2011 dictall.com