User:EGM6321.F10.TEAM1.WILKS/Mtg37

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EGM6321 - Principles of Engineering Analysis 1, Fall 2009[edit]

Mtg 37: Thurs, 17Nov09


Page 37-1

[edit]

P.36-4 continued







From P.18-1 :

(1)



HW show END HW

ref K p33 for

(2)



is odd

HW Use Eq(2) to show when is even or odd, depending on "n" END HW

HW Plot and END HW

Legendre function or solution of Legendre solution

Page 37-2

[edit]

(1)

for

for

HW for END HW

Eq.(3) P.33-1

for

Proof: Legendre equation, Eq.(1) P.14-2 : 2)

Where

(2)





Multiply by and integrate from -1 to +1:



Where


Page 37-3

[edit]

Integrate by parts:

(1)



Interchange n and m:

(2)



Eq(1)-Eq(2):



Where since

when

cf.K.p41

References[edit]