# Accession Number:

## AD0870495

# Title:

## The Numerical Evaluation of a Certain Integral with a Rapidly Oscillating Integrand.

# Descriptive Note:

## Technical memo.,

# Corporate Author:

## SACLANT ASW RESEARCH CENTRE LA SPEZIA (ITALY)

# Personal Author(s):

# Report Date:

## 1970-03-15

# Pagination or Media Count:

## 24.0

# Abstract:

This Memorandum considers the numerical evaluation of integrals of the form over the range from 0 to t, the integral eto the alpha times S power, times sin 2Wsub 0S, times the -32 power of the quantity d squared the square of Ysub 0-VS, times ds by two methods. The first is conventional. The second is unconventional and exploits the possibility of expanding the expression dsquared Ysub 0-VSSquared in terms of Legendre polynomials. The integrals whose evaluation is discussed, arose in the study of the following problem. A sinusoidal source, with strength that falls off as the inverse cube of the distance from the source, moves in a straight line past a receiver with velocity much smaller than the field propagation velocity.

# Descriptors:

- *INTEGRALS
- *WAVE PROPAGATION
- MATHEMATICAL MODELS
- OSCILLATION
- WAVEFORM GENERATORS
- ALGORITHMS
- NUMERICAL METHODS AND PROCEDURES
- POLYNOMIALS
- TABLES(DATA)
- SERIES(MATHEMATICS)
- CONVERGENCE
- INFORMATION THEORY
- UNDERWATER SOUND
- ACOUSTIC DETECTORS
- RADIO WAVES
- RADIO RECEIVERS
- COMPUTER PROGRAMMING
- NETWORKS
- VELOCITY
- MOTION
- ERRORS
- INTEGRAL EQUATIONS

# Subject Categories:

- Theoretical Mathematics
- Cybernetics
- Radiofrequency Wave Propagation