Transactions of the Cambridge Philosophical Society, المجلد 22University Press, 1923 |
من داخل الكتاب
النتائج 1-5 من 100
الصفحة 11
... follows : - ( D ̧ ́1 ) 2 ( D ̧11 ) . ( D ̧2 ) 2 ( D ̧2 ) . B ̧2В1 = 87 , ( D ̧§1 ) ) 2 ( D ̧2 ) . B ̧2 B ̧ = ( D ̧2 ) ( D ̧2 ) ( 2 ̧ ̧ +  ̧ ̧2 ̧ ) 4 4 = A ̧Ð ̧o ( 2A ̧Â1 + 2A1В1B ̧ + 2 ̧¿Â1⁄2 +  ̧ ̧2В2 ) = 1 4 1 = A , 2 ( ...
... follows : - ( D ̧ ́1 ) 2 ( D ̧11 ) . ( D ̧2 ) 2 ( D ̧2 ) . B ̧2В1 = 87 , ( D ̧§1 ) ) 2 ( D ̧2 ) . B ̧2 B ̧ = ( D ̧2 ) ( D ̧2 ) ( 2 ̧ ̧ +  ̧ ̧2 ̧ ) 4 4 = A ̧Ð ̧o ( 2A ̧Â1 + 2A1В1B ̧ + 2 ̧¿Â1⁄2 +  ̧ ̧2В2 ) = 1 4 1 = A , 2 ( ...
الصفحة 16
... follows : ( i ) That a number , h1 , exists such that ( s ) is analytic on the right of the line ( ii ) R ( 28 ) = h1 . That numbers and λ exist such that y ' > 0 , 0 < λ < π and such that when | 8 | ≥ y ' , │arg ( s / a ) < λ + 1π ...
... follows : ( i ) That a number , h1 , exists such that ( s ) is analytic on the right of the line ( ii ) R ( 28 ) = h1 . That numbers and λ exist such that y ' > 0 , 0 < λ < π and such that when | 8 | ≥ y ' , │arg ( s / a ) < λ + 1π ...
الصفحة 27
... follows without difficulty from ( 10 ) . ( C ) Let A = 2 cos y , i.e. | a1 | = 1 . ( A ‡ 0 . ) By taking q = 1 , we get the expansion ( 13 ) as before , valid over the region - π cos y < sin y log | z | - cos y arg z < π COS Y. That is ...
... follows without difficulty from ( 10 ) . ( C ) Let A = 2 cos y , i.e. | a1 | = 1 . ( A ‡ 0 . ) By taking q = 1 , we get the expansion ( 13 ) as before , valid over the region - π cos y < sin y log | z | - cos y arg z < π COS Y. That is ...
الصفحة 33
... follows , without difficulty , from Stirling's formula . ) Now if we have a finite number of asymptotic expansions with the same ' characteristics , ' their product may be represented by an asymptotic expansion with the same ...
... follows , without difficulty , from Stirling's formula . ) Now if we have a finite number of asymptotic expansions with the same ' characteristics , ' their product may be represented by an asymptotic expansion with the same ...
الصفحة 34
... follows that , for any fixed value of y ( i.e. any value not depending on k ) , that is to say , 8 Σ Bk , n yn n = o ( n + 0 ) .n ! - 0 as k < -8 ; F ( y ) = yh + 1 Σ bm Gb ( y ; 0 , m ; M , c ) . m = 0 Taking to be any fixed integer ...
... follows that , for any fixed value of y ( i.e. any value not depending on k ) , that is to say , 8 Σ Bk , n yn n = o ( n + 0 ) .n ! - 0 as k < -8 ; F ( y ) = yh + 1 Σ bm Gb ( y ; 0 , m ; M , c ) . m = 0 Taking to be any fixed integer ...
طبعات أخرى - عرض جميع المقتطفات
عبارات ومصطلحات مألوفة
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