The name is absent



Rectilinear Drawing          67

which we write in the form

fo'⅛(r sin χ)(cos χ cos χ - sin χ sin χ')dχ=0.

On integrating by parts the first term evidently takes the
form

1 [

-   ∕2w (r sin χ) sin χdχ,

rJo

while the second is seen to be equal to
d f

-jf I fz'^'' (r sɪn χ) sin χdχ.

Hence if we write

W = X*7?0 (r sin χ) sin χdχ,

we conclude that

1jγ-jγ≡o,

r

i.e., W = cτ. But since /Fz(0) =0 we must have c =0, and so
F≡0.

Employing now the same argument as in the case m = 1,
for the equation
W = Owe find that f∙ι's) =0 and so ∕a(j,)≡0.

Likewise we readily infer that gs(∕)≡O.

More generally, we may obtain the stated result for
m = 1, 2 ■ ∙ ∙ in succession, by writing at the mth stage

cos =cos χ cos (tn — l)χ —sin χ sin (m-l')χ
sin =sin χ cos (m — l)χ+ cos χ sin (m-l)χ

in the equations involving ∕m(j) and gm(j∙) respectively, and
thus reducing the question to one of the type considered at
the (tn —l)st stage.

In this manner the stated result is readily established.

We are now in a position to formulate preliminary neces-
sary and sufficient conditions for a continuous solution of the
general harmonic case of the
mth order.



More intriguing information

1. WP 36 - Women's Preferences or Delineated Policies? The development or part-time work in the Netherlands, Germany and the United Kingdom
2. The name is absent
3. The name is absent
4. Can a Robot Hear Music? Can a Robot Dance? Can a Robot Tell What it Knows or Intends to Do? Can it Feel Pride or Shame in Company?
5. Industrial Cores and Peripheries in Brazil
6. Barriers and Limitations in the Development of Industrial Innovation in the Region
7. The name is absent
8. Public-Private Partnerships in Urban Development in the United States
9. Popular Conceptions of Nationhood in Old and New European
10. Computational Batik Motif Generation Innovation of Traditi onal Heritage by Fracta l Computation