Remote-Sensing Technologies and Data Processing Algorithms - New Ecoinformatics Tools in Environmental Science: Applications and Decision-making - page 195

Equate the integral in ( 2.18 ) to zero. It gives
T ð h Þ ¼c Z

c k ð h Þ dh ;

where c is an arbitrary constant. The integral in ( 2.18 ) will be equal to zero if

X

n

c 1 k B k k ð k 1 Þ k !

k ¼ 0

ð 2 : 19 Þ

k ¼ 2

Further integrating of ( 2.18 ) by parts gives

where

T 000 ð h Þc k ð h Þ 3T 00 ð h Þc k ð h Þ T 0 ð h Þc 0 k ð h Þþ 3T 0 ð h Þ c 0 k 2
c

Z 1

J 3 ¼ F k ð h Þ dh

4
k

0

This integral will be equal to zero at
T ð h Þ ¼c Z

Z

c k ð h Þ c k ð u Þ dudh

If the condition ( 2.16 ) is not met then J 3 =0at
X

n

c 2 k
k

B k k ð k 1 Þð k 2 Þ k ! ¼ 0

k¼3

With the process of integration of ( 2.18 ) continued N times, we obtain

ð 2 : 20 Þ

where

P 2 ð h Þ ¼T 0 ð h Þ=c k ð h Þ...; P k ð h Þ ¼P 0 k 1 ð h Þ=c k ð h Þ P 1 ð h Þ ¼T ð h Þ;

but

Z 1

P 0 N ð h Þ F k ð h Þ dh ¼ 0

J N ¼

0