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Chapter 11: Q3P (page 548)

Prove that erf(x) is an odd function of x. Hint: Put t = -s in (9.1) .

Short Answer

Expert verified

It has been proved that the erf(x) is an off function of x .

Step by step solution

01

Definition of error of function

The error of the function is defined as (x)=2蟺鈭�0xe-t2dt.

02

Prove that error is odd

The value of integration is erf(x)=2蟺鈭�0xe-t2dt.

Substitute -x in place of x .

erf(-x)=2蟺鈭�0-xe-t2dt

Let u = -s , then du = -ds .

The equation becomes as follows:

erf(-x)=2蟺鈭�0xe-s2-dserf(-x)=-erf(x)

Hence, the statement has been proved.

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Most popular questions from this chapter

Express the complementary error function erfc(x)as an incomplete螕'function (see Problem 2) and use your result in Problem 2to obtain (again) the asymptotic expansion oferfc(x) as in (10.4) .
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