MCQs of Series Solutions of ODEs and Special Functions (Mathematics - II - 3110015)

Showing 11 to 20 out of 40 Questions

11.

The polynomial

2 x^{2} - 4 x + 3

in terms of Legendre’s polynomial is ......

12.

The Rodrigues' formula for Legendre's polynomial of degree

n

P_{n} (x) = m \frac{d^{n}}{d x^{n}} (x^{2} - 1)^{n}

. Then

m

is .....

13.

The generating function of the Legendre’s polynomial is

\sum_{n = 0}^{\infty} P_{n} (x) \cdot t^{n} =

..........

14.

The value of

P_{n} (- 1) =

.....

15.

Let

P_{0}

P_{1}

and

P_{2}

be the Legendre’s polynomials of order 0,1 and 2 respectively. Which of the following statement is correct?

16.

Let the Legendre's polynomial

P_{4} (x) = λ (- x^{4} + \frac{30}{35} x^{2} - \frac{3}{35})

. Then

λ =

.....

17.

The Bessel's function of the first kind of order

n

is denoted by

J_{n} (x)

and defined as .....

(a)	$\sum_{k = 0}^{\infty} \frac{(- 1)^{k}}{k! Γ (n + 1 + k)} {(\frac{x}{2})}^{n - 2 k}$
(b)	$\sum_{k = 0}^{\infty} \frac{(- 1)^{k}}{k! Γ (n + k)} {(\frac{x}{2})}^{n + 2 k}$
(c)	$\sum_{k = 0}^{\infty} \frac{(- 1)^{k}}{k! Γ (n + 1 + k)} {(\frac{x}{2})}^{n + 2 k}$
(d)	$\sum_{k = 0}^{\infty} \frac{(- 1)^{k}}{Γ (n + 1 + k)} {(\frac{x}{2})}^{n + 2 k}$

18.

Which of the following property is correct for

J_{n} (x)

19.

J_{(- \frac{1}{2})} (x) =

.....

20.

Which of the following relation is correct for

J_{n} (x)

Showing 11 to 20 out of 40 Questions