 12.6.1: Find the first four ai > 0 defined by J1(3a) = 0.
 12.6.2: Find the first four ai;:::: 0 defined by J0(2a) = 0.
 12.6.3: J0(2a) = 0
 12.6.4: J0(2a) = 0
 12.6.5: J0(2a) + 2al0(2a) = 0
 12.6.6: J0(2a) + a J0(2a) = 0
 12.6.7: f(x) = 5x, 0 < x < 4 311(4a) + 4al1(4a) = 0
 12.6.8: f(x) = x2, 0 < x < 1 12 (a) = 0
 12.6.9: f(x) = x2, 0 < x < 3 J0(3a) = 0
 12.6.10: f(x) = 1  x2, 0 < x < 1 10(a) = 0
 12.6.11: (a) Use aCAStography = 3J1(x) + xJ!(x) onaninterval sothat the firs...
 12.6.12: (a) Use the values of ai in part ( c) of and a CAS to approximate t...
 12.6.13: If the partial sums in are plotted on a symmetric interval such as ...
 12.6.14: (a) Sketch, by hand, a graph of what you think the FourierBessel se...
 12.6.15: f(x) = {O, 1 < x < 0 x, 0 < x < 1
 12.6.16: f(x) = eX, 1 < x < 1
 12.6.17: The first three Legendre polynomials are P 0(x) = 1, P 1 (x) = x, a...
 12.6.18: Use the results of to find a FourierLegendre expansion (23) of F((...
 12.6.19: A Legendre polynomial Pix) is an even or odd function, depending on...
 12.6.20: Show that ifjis an odd function on the interval (1, 1), then (21) ...
 12.6.21: f(x) = x, 0 < x < 1; (25)
 12.6.22: f(x) = 1, 0 < x < 1; (27)
 12.6.23: Why is a FourierLegendre expansion of a polynomial function that i...
 12.6.24: Use your conclusion from to find the finite FourierLegendre series...
Solutions for Chapter 12.6: Bessel and Legendre Series
Full solutions for Advanced Engineering Mathematics  5th Edition
ISBN: 9781449691721
Solutions for Chapter 12.6: Bessel and Legendre Series
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Advanced Engineering Mathematics , edition: 5. Advanced Engineering Mathematics was written by and is associated to the ISBN: 9781449691721. Chapter 12.6: Bessel and Legendre Series includes 24 full stepbystep solutions. Since 24 problems in chapter 12.6: Bessel and Legendre Series have been answered, more than 33127 students have viewed full stepbystep solutions from this chapter.

Alternative hypothesis
In statistical hypothesis testing, this is a hypothesis other than the one that is being tested. The alternative hypothesis contains feasible conditions, whereas the null hypothesis speciies conditions that are under test

Analytic study
A study in which a sample from a population is used to make inference to a future population. Stability needs to be assumed. See Enumerative study

Assignable cause
The portion of the variability in a set of observations that can be traced to speciic causes, such as operators, materials, or equipment. Also called a special cause.

Attribute control chart
Any control chart for a discrete random variable. See Variables control chart.

Average
See Arithmetic mean.

Biased estimator
Unbiased estimator.

Bivariate distribution
The joint probability distribution of two random variables.

Box plot (or box and whisker plot)
A graphical display of data in which the box contains the middle 50% of the data (the interquartile range) with the median dividing it, and the whiskers extend to the smallest and largest values (or some deined lower and upper limits).

Chisquare (or chisquared) random variable
A continuous random variable that results from the sum of squares of independent standard normal random variables. It is a special case of a gamma random variable.

Coeficient of determination
See R 2 .

Conditional probability density function
The probability density function of the conditional probability distribution of a continuous random variable.

Conditional probability mass function
The probability mass function of the conditional probability distribution of a discrete random variable.

Correlation matrix
A square matrix that contains the correlations among a set of random variables, say, XX X 1 2 k , ,…, . The main diagonal elements of the matrix are unity and the offdiagonal elements rij are the correlations between Xi and Xj .

Cumulative distribution function
For a random variable X, the function of X deined as PX x ( ) ? that is used to specify the probability distribution.

Curvilinear regression
An expression sometimes used for nonlinear regression models or polynomial regression models.

Degrees of freedom.
The number of independent comparisons that can be made among the elements of a sample. The term is analogous to the number of degrees of freedom for an object in a dynamic system, which is the number of independent coordinates required to determine the motion of the object.

Deining relation
A subset of effects in a fractional factorial design that deine the aliases in the design.

Discrete random variable
A random variable with a inite (or countably ininite) range.

Factorial experiment
A type of experimental design in which every level of one factor is tested in combination with every level of another factor. In general, in a factorial experiment, all possible combinations of factor levels are tested.

False alarm
A signal from a control chart when no assignable causes are present