Find the value of

8. Evaluate

Prove that = n

6. Write the formula for .

Define Beta and Gamma function.

8. Show that .

Define Beta function.

6. Compute

Write the formula for .

6. Evaluate

Evaluate

6. Evaluate

7. Prove that

8. Show that

1. Evaluate

2. State any two properties of Beta function.

3. Define Beta and Gamma functions.4.

5. 6. Prove that

6. Prove that ( + 1) = .7.8. 6. Define (m, n) and prove (m, n) = (n, m).

What is the reduction formula for (n)?

6. Define Beta function.

Give two integers such that their Gamma values are equal.

6. Write in terms of Beta integral.

Define Gamma and Beta function.

6. Prove that

(a) Using Beta and Gamma functions evaluate

where ‘n’ is positive integer.

(b) Evaluate

(or)

18. (a) Prove that

(b) Evaluate

(a) Prove that .Hence find .

(b) Show that .

(a) Evaluate in terms of gamma function and

hence find .

(b) Find the value of over the positive

quadrant of the ellipse in terms of gamma

function.

Prove that where m,n > 0.

(or)

16. Express in terms of Gamma functions and

evaluate .

(a) Prove that .Hence find .

(b) Show that .

Prove that (m,n) =

1. (a) Prove that

(b) Show that

(or)

(b) Express in terms of Gamma function

Prove that (m,n) = Hence deduce that (m,n) =

.

(or)

16. Express in terms of Gamma functions.

Hence Evaluate

Using Beta and Gamma function, show that for any positive integer m

(a)

(b)

(or)

16. (a) Explain in terms of Beta function and hence

evaluate

(b) Evaluate in terms of Gamma function.

(a) Prove that (m,n) = .

(b) Evaluate cosmx sinn x dx, where m of n is even

integers.(or)

16. (a) Prove that (n+ ½)=

(b) Prove that (n,n) = .

(a) Prove that β(m, n) = m n/m+n

(b) Evaluate in terms of Gamma function.

(a) Evaluate in terms of Gamma functions and hence find

(b) Show the volume of the region of space bounded by the co-

ordinate planes and the surface

(or)

16. (a) Prove that