In Chapter 12, equations (5.1) and ( 5.2 ) , we expanded the function ϕ ( x , h ) in a series of powers of h . Use Theorem III (see instructions for Problems 34 to 42 above) to show that the series for ϕ ( x , h ) converges for | h | < 1 and − 1 ≤ x ≤ 1. Here h is the variable and x is a parameter; you should find the (complex) value of h which makes Φ infinite, and show that the absolute value of this complex number is 1 (independent of x when x 2 ≤ 1 ). This proves that the series for real h converges for | h | < 1 .
In Chapter 12, equations (5.1) and ( 5.2 ) , we expanded the function ϕ ( x , h ) in a series of powers of h . Use Theorem III (see instructions for Problems 34 to 42 above) to show that the series for ϕ ( x , h ) converges for | h | < 1 and − 1 ≤ x ≤ 1. Here h is the variable and x is a parameter; you should find the (complex) value of h which makes Φ infinite, and show that the absolute value of this complex number is 1 (independent of x when x 2 ≤ 1 ). This proves that the series for real h converges for | h | < 1 .
In Chapter 12, equations (5.1) and
(
5.2
)
,
we expanded the function
ϕ
(
x
,
h
)
in a series of powers of
h
.
Use Theorem III (see instructions for Problems 34 to 42 above) to show that the series for
ϕ
(
x
,
h
)
converges for
|
h
|
<
1
and
−
1
≤
x
≤
1.
Here
h
is the variable and
x
is a parameter; you should find the (complex) value of
h
which makes
Φ
infinite, and show that the absolute value of this complex number is 1 (independent of
x
when
x
2
≤
1
). This proves that the series for real
h
converges for
|
h
|
<
1
.
Combination of a real number and an imaginary number. They are numbers of the form a + b , where a and b are real numbers and i is an imaginary unit. Complex numbers are an extended idea of one-dimensional number line to two-dimensional complex plane.
Using & Understanding Mathematics: A Quantitative Reasoning Approach (7th Edition)
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