Legendre Polynomials Quiz

What is the definition of Legendre polynomials in terms of the nth derivative of a function?

• The nth logarithm of x squared minus 1 to the n

• The nth derivative of x squared minus 1 to the n

• The nth integral of x squared minus 1 to the n

• The nth square root of x squared minus 1 to the n

What is the interval of interest for Legendre polynomials based on their definition?

• -1 to 1

• 0 to 2

• -2 to 2

• 1 to 3

Which type of Legendre polynomials correspond to even functions?

• Composite values of n

• Prime values of n

• Odd values of n

• Even values of n

What is the highest order term in the Legendre polynomial for n=3?

• 1

• x cubed

• x squared

• x

What is the generating function for Legendre polynomials?

• Power series with Legendre polynomials as coefficients

• Maclaurin series with Legendre polynomials as coefficients

• Fourier series with Legendre polynomials as coefficients

• Taylor series with Legendre polynomials as coefficients

What are the zeros of the Legendre polynomial function?

• Plus and minus 4

• Plus and minus 3

• Plus and minus 1

• Plus and minus 2

Which type of Legendre polynomials correspond to odd functions?

• Even values of n

• Composite values of n

• Prime values of n

• Odd values of n

What is the normalizing factor in the definition of Legendre polynomials?

• 2 over n factorial

• 1 over n factorial

• n over 2 factorial

• n factorial