0195136047.pdf

(Joyce) #1

850 APPENDIX G



π^2
4

sin

4 πt
k

+(

π^2
5


4
53

)sin

5 πt
k

+...

]
( 0 <t<k) (30)

t^2 =

k^2
3


4 k^2
π^2

[
cos

πt
k


1
22

cos

2 πt
k

+

1
32

cos

3 πt
k


1
42

cos

4 πt
k

+...

]
(−k<t<k) (31)

1 −

1
3

+

1
5


1
7

+...=

π
4

(32)

1 +

1
22

+

1
32

+

1
42

+...=

π^2
6

(33)

1 −

1
22

+

1
32


1
42

+...=

π^2
12

(34)

1 +

1
32

+

1
52

+

1
72

+...=

π^2
8

(35)

1
22

+

1
42

+

1
62

+

1
82

+...=

π^2
24

(36)
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