Transactions of the Cambridge Philosophical Society, المجلد 22University Press, 1923 |
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النتائج 1-5 من 33
الصفحة 24
... vanish . ) ... From this expansion , we may shew that F ( y ) can be expressed as the sum of a series of functions of the type G ( y ; 0 , k ) ; for we have k ∞ F ( y ) = Σ Σ where bk , n = amyn m = 0 n = h + 1 ( n + ✪ ) 3 l ' ( n + m ...
... vanish . ) ... From this expansion , we may shew that F ( y ) can be expressed as the sum of a series of functions of the type G ( y ; 0 , k ) ; for we have k ∞ F ( y ) = Σ Σ where bk , n = amyn m = 0 n = h + 1 ( n + ✪ ) 3 l ' ( n + m ...
الصفحة 28
... vanish , so also do the first B ' of the B coefficients So , S1 , ... ; it will , therefore , be possible to modify the above expansion slightly when ẞ is a positive integer and not zero ; we shall not carry out this modification , as a ...
... vanish , so also do the first B ' of the B coefficients So , S1 , ... ; it will , therefore , be possible to modify the above expansion slightly when ẞ is a positive integer and not zero ; we shall not carry out this modification , as a ...
الصفحة 33
... vanish ; this is evident when we consider the effect of making sin ( 21 ) . From ( 9 ) and ( 21 ) it follows that F ( y ) = yh + 1 & yn 00 уп 1 n = on ! ( n + 0 ) b bo + b1 + k m = 0 | Bk , n│ Bk , n = bk + 1 where = yh + 1 Σ bm Gb ( y ...
... vanish ; this is evident when we consider the effect of making sin ( 21 ) . From ( 9 ) and ( 21 ) it follows that F ( y ) = yh + 1 & yn 00 уп 1 n = on ! ( n + 0 ) b bo + b1 + k m = 0 | Bk , n│ Bk , n = bk + 1 where = yh + 1 Σ bm Gb ( y ...
الصفحة 36
... vanish , we see that the first 1 + h + B ' -b of the coefficients To , T1 , ... vanish , and so it is convenient to take 1 + h + B ' - b . 13. It is easy to see that the nth of the coefficients To , T , ... ( commencing with the first ...
... vanish , we see that the first 1 + h + B ' -b of the coefficients To , T1 , ... vanish , and so it is convenient to take 1 + h + B ' - b . 13. It is easy to see that the nth of the coefficients To , T , ... ( commencing with the first ...
الصفحة 37
... vanish . + cn is supposed to be finite when n is such that ( 8 ) is not analytic near s = n . Proc . Lond . Math . Soc . , ser . 2 , vol . v . ( 1906 ) , pp . 59-118 . § See Barnes , Quart . Journ . Math . vol . xxxi . ( 1899 ) , pp ...
... vanish . + cn is supposed to be finite when n is such that ( 8 ) is not analytic near s = n . Proc . Lond . Math . Soc . , ser . 2 , vol . v . ( 1906 ) , pp . 59-118 . § See Barnes , Quart . Journ . Math . vol . xxxi . ( 1899 ) , pp ...
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a₁ angle approximately asymptotic expansion atmosphere Axiom of Archimedes axis b₁ c₁ calculated coefficients considered constant convergent convex set cordon corresponding cos² curve d₁ definition denote density determined differential equations disturbance diurnal diurnal variations dyadic earth equal escape expression factor finite follows formula free path function G. H. Hardy giant star given h₂ Hence integral equation invariant Jacobian k₁ k₂ magnitude molecules obtained orbit paper parameters partitions plane positive potential Primitive Roots ratio relation respectively result rotation scalar shew shewn sin² solar solid angle solutions substitution suppose surface t₁ theorem theory v₁ values vector velocity w₁ X₁ XXII zero Σ Σ дх