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Chapter 11: Q17P (page 540)

Express as a function

Short Answer

Expert verified

The solution to this problem is

Step by step solution

01

Given Information

The given information is the gamma function to be used in the solution.

The given integral is

02

Definition of Gamma function

To extend the factorial to any real number x>0 (whether or not the real number is a whole number), the gamma function is defined as for .

03

Find the solution

Use substitution method to solve the integral.

Let , then we have,

The given integral is now in the form of .

Express the integral in gamma function, and then evaluate the gamma function and integral numerically.

The Gamma function is for . Then solve for the given function as follow:

Hence, the solution to this problem is

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Most popular questions from this chapter

Express the following integrals as 尾functions, and then, by (7.1), in terms of 螕 functions. When possible, use 螕 function formulas to write an exact answer in terms of 蟺,2, etc. Compare your answers with computer results and reconcile any discrepancies.

3. 鈭�0111-x3dx.

Show that for integral n, m,

1/B(n,m)=m(n+m-1n-1)=n(n+m-1m-1)

Hint: See Chapter 1, Section 13C, Problem 13.3.

Ifu=ln(sec蠁+tan蠁), then 蠁 is a function of u called the Gudermannian of u, 蠁=gdu. Prove that: .

u=lntan(蟺4+蠒2),tangdu=sinhu,singdu=tanhu,ddugdu=sechu

Use the recursion relation (3.4), and if needed, equation (3.2) to simplify:

螕(23)/螕(83)

Use Stirling鈥檚 formula to evaluatelimn鈫�鈭�(2n)!n22n(n!)2.
See all solutions

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