N-DIMENSIONAL HARMONIC-OSCILLATOR YIELDS MONOTONIC SERIES FOR THE MATHEMATICAL CONSTANT-PI

被引：6

作者：

LYNCH, R ^{[1
]}

MAVROMATIS, HA ^{[1
]}

机构：

[1] KING FAHD UNIV PETR & MINERALS,DEPT PHYS,DHAHRAN 31261,SAUDI ARABIA

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 1990年 / 30卷 / 02期

关键词：

N-dimensional harmonic oscillator; Series for π;

D O I：

10.1016/0377-0427(90)90021-Q

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Recently, Mavromatis (1990) has shown that the usual quantum mechanical ideas of matrix elements, expansion in complete sets, and the like, coupled to the three-dimensional harmonic oscillator problem, lead to an infinite set of series expansions for the mathematical constant π. In this paper his results are extended by considering a harmonic oscillator in a general space of N dimensions. It is found that in each odd dimension one obtains series for π, while in each even dimension, series for 1/π. © 1990.

引用

页码：127 / 137

页数：11

共 10 条

[1] Borwein J. M., 1986, PI AGM STUDY ANAL NU
[2] MATRIX ELEMENTS OF NUCLEON-NUCLEON POTENTIAL FOR USE IN NUCLEAR-STRUCTURE CALCULATIONS
ELLIOTT, JP
JACKSON, AD
MAVROMAT.HA
SANDERSO.EA
SINGH, B
[J]. NUCLEAR PHYSICS A, 1968, A121 (02) : 241 - &
[3] Erdelyi A., 1953, HIGH TRANSCENDENTAL, VI, p[3, 56]
[4] EVES H, 1976, INTRO HIST MATH, P96
[5] EXTON H, 1976, MULTIPLE HYPERGEOMET, P18
[6] GRADSHTEYN IS, 1980, TABLE INTEGRALS SERI, P337
[7] 2 DOUBLY INFINITE SETS OF SERIES FOR PI
MAVROMATIS, HA
[J]. JOURNAL OF APPROXIMATION THEORY, 1990, 60 (01) : 1 - 10
[8] PI IN THE SKY
MERMIN, ND
[J]. AMERICAN JOURNAL OF PHYSICS, 1987, 55 (07) : 584 - 585
[9] MERZBACHER E, 1970, QUANTUM MECHANICS, P71
[10] MULLER C, 1966, LECTURE NOTES MATH, V17

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