Transactions of the Cambridge Philosophical Society, المجلد 22University Press, 1923 |
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النتائج 1-5 من 78
الصفحة 16
... satisfy the inequalities | αx | < H. г ( k ) . k " { log ( k + 1 ) } 3 . | ak | < H. г ( k ) . { log ( k + 1 ) } B ... satisfied if be a member of a very large class of functions which can easily be constructed . Some examples are ...
... satisfy the inequalities | αx | < H. г ( k ) . k " { log ( k + 1 ) } 3 . | ak | < H. г ( k ) . { log ( k + 1 ) } B ... satisfied if be a member of a very large class of functions which can easily be constructed . Some examples are ...
الصفحة 19
... satisfied by | I | , | 12 | , | Is \ . Let us first consider I ; on PQ we have the following inequalities satisfied : y y y .. ( 4a ) , log ( 1-2 ) > K , ( 1-2 ) > K , arg - log ( 1- < K , arg ( 1-2 ) < K ; — Ꮖ also R ( x − y ) < 0 ...
... satisfied by | I | , | 12 | , | Is \ . Let us first consider I ; on PQ we have the following inequalities satisfied : y y y .. ( 4a ) , log ( 1-2 ) > K , ( 1-2 ) > K , arg - log ( 1- < K , arg ( 1-2 ) < K ; — Ꮖ also R ( x − y ) < 0 ...
الصفحة 23
... satisfied we may shew that I is 0 ( x ) where L is the value of R ( as ) / R ( a ) on the contour D. Further , we may shew , by Cauchy's theorem , that I , is equal to minus the sum of the residues of the integrand at those poles which ...
... satisfied we may shew that I is 0 ( x ) where L is the value of R ( as ) / R ( a ) on the contour D. Further , we may shew , by Cauchy's theorem , that I , is equal to minus the sum of the residues of the integrand at those poles which ...
الصفحة 26
... satisfied if q = 1 . In other words , if a 1 < 1 and sin y log | z | - cos y arg z < TA , then f ( x ) possesses the asymptotic expansion - f ( x ) = exp ( x1a @ga ) 1 / a αβία ρυβία n = 0 Sn . T ( 1 - B ) xn / a egna +0 ( x - viα 1 ) ...
... satisfied if q = 1 . In other words , if a 1 < 1 and sin y log | z | - cos y arg z < TA , then f ( x ) possesses the asymptotic expansion - f ( x ) = exp ( x1a @ga ) 1 / a αβία ρυβία n = 0 Sn . T ( 1 - B ) xn / a egna +0 ( x - viα 1 ) ...
الصفحة 27
... satisfied ; so that with this determination of arg z and arg x we have -Asin y log | 2 - cos y arg z < † πA R ( aega ) > 0 , arg ( aega ) < } π ; | | and then ( 7a ) is satisfied since cos y ( q cos y − A ) | ≥ 0 . - - .. ( 16a ) ...
... satisfied ; so that with this determination of arg z and arg x we have -Asin y log | 2 - cos y arg z < † πA R ( aega ) > 0 , arg ( aega ) < } π ; | | and then ( 7a ) is satisfied since cos y ( q cos y − A ) | ≥ 0 . - - .. ( 16a ) ...
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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