ISSN:
1089-7658
Quelle:
AIP Digital Archive
Thema:
Mathematik
,
Physik
Notizen:
The following inequality is established: ||Pn(cos cursive-theta)||〈 [(square root of)1+(π4/16)(n+1/2)4 sin4 cursive-theta]−1, 0〈cursive-theta〈π, n=1,2,..., where Pn(x) denotes the Legendre polynomial of degree n. The relation P2n(cos cursive-theta) + (4/π2)× Q2n(cos cursive-theta) 〈 [(square root of)1+(π4/16)(n+1/2)4 sin4 cursive-theta]−1, n=1,2,..., on [θn1,θn,n+1], is proven where Qn(x) denotes the Legendre function of second kind, cos θn1 the largest zero of Qn(x), and cos θn,n+1=−cos θn1. Similarly we obtain the inequalities ||J0(x)|| 〈 [(square root of)1+(π4/16)x4]−1, x≠0, and J20(x) + Y20(x)〈 [(square root of)1+(π4/16)x4]−1, x≥y1, where y1=0.893577... is the first positive zero of Y0(x), and J0(x), Y0(x) denote the Bessel functions of the first and second kind, respectively. The results of the present paper arise out of some problems of nuclear and particle physics.
Materialart:
Digitale Medien
URL:
http://dx.doi.org/10.1063/1.530873
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