Transactions of the Cambridge Philosophical Society, المجلد 22University Press, 1923 |
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الصفحة 3
... have either of the two expressions Dm , Dm , ... Dex hx1 h x2 ... h2 = 1 DX1 Dx2 ΧΙ X1 Dεx hx2 ... Dε h2 h2 ... 2 hex⋅ The expressions are equivalent and may be evaluated by means 1-2 MAJOR MACMAHON , ON COMPOUND DENUMERATION . 3.
... have either of the two expressions Dm , Dm , ... Dex hx1 h x2 ... h2 = 1 DX1 Dx2 ΧΙ X1 Dεx hx2 ... Dε h2 h2 ... 2 hex⋅ The expressions are equivalent and may be evaluated by means 1-2 MAJOR MACMAHON , ON COMPOUND DENUMERATION . 3.
الصفحة 4
Cambridge Philosophical Society. The expressions are equivalent and may be evaluated by means of theorems given ( loc . cit . ) . The whole number of partitions of the bipart ( pq ) is in consequence ΣΣ Dm , Day DT ... DΣx hx , hx2 ...
Cambridge Philosophical Society. The expressions are equivalent and may be evaluated by means of theorems given ( loc . cit . ) . The whole number of partitions of the bipart ( pq ) is in consequence ΣΣ Dm , Day DT ... DΣx hx , hx2 ...
الصفحة 8
... Ex and ... AΣπ - Ex + 5 X1 azπ - 2x + 3 ( x + 1 ) terms , whilst if Ex be even Ex - 1 terms respectively . That these two series are equivalent may be shewn algebraically 8 MAJOR MACMAHON , ON COMPOUND DENUMERATION .
... Ex and ... AΣπ - Ex + 5 X1 azπ - 2x + 3 ( x + 1 ) terms , whilst if Ex be even Ex - 1 terms respectively . That these two series are equivalent may be shewn algebraically 8 MAJOR MACMAHON , ON COMPOUND DENUMERATION .
الصفحة 9
Cambridge Philosophical Society. That these two series are equivalent may be shewn algebraically as follows . For brevity put Eπ - Ex = 0 and note that Σαχ D1ax , ax ̧ ... ao + 1 = ax , ax2 ... αo + Σax1 - 1 ax , ... αo +1 , D2axax2 Dax ...
Cambridge Philosophical Society. That these two series are equivalent may be shewn algebraically as follows . For brevity put Eπ - Ex = 0 and note that Σαχ D1ax , ax ̧ ... ao + 1 = ax , ax2 ... αo + Σax1 - 1 ax , ... αo +1 , D2axax2 Dax ...
الصفحة 44
... equivalent but not identical . The force R and couple M exerted on the journal by the liquid , the force R ' and couple M ' exerted by the liquid on the bearing , the force R " and couple M " applied to the bearing to keep it in ...
... equivalent but not identical . The force R and couple M exerted on the journal by the liquid , the force R ' and couple M ' exerted by the liquid on the bearing , the force R " and couple M " applied to the bearing to keep it in ...
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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