Transactions of the Cambridge Philosophical SocietyUniversity Press, 1912 |
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الصفحة v
... transformation 176 Laplace 479 Lebesgue 365 Lerch 185 Leudesdorf 159 Levi - Civita 173 , 187 Linear differential equations and definite integrals ( Bateman ) 171 Littlewood , J. E. , On a class of integral functions 301 Littlewood 282 ...
... transformation 176 Laplace 479 Lebesgue 365 Lerch 185 Leudesdorf 159 Levi - Civita 173 , 187 Linear differential equations and definite integrals ( Bateman ) 171 Littlewood , J. E. , On a class of integral functions 301 Littlewood 282 ...
الصفحة viii
... transformation expressed by the equation ( 2 ) is valid if lim to e - T * dx Σ ƒn ( x ) = lim Σ t → 0 10 -TX e - τx ƒn ( x ) dx = Σ lim [ * e * ƒn ( x ) dx . t- Now the first of these equations asserts that the series 2 MR HARDY ...
... transformation expressed by the equation ( 2 ) is valid if lim to e - T * dx Σ ƒn ( x ) = lim Σ t → 0 10 -TX e - τx ƒn ( x ) dx = Σ lim [ * e * ƒn ( x ) dx . t- Now the first of these equations asserts that the series 2 MR HARDY ...
الصفحة ix
... transformation asserts G [ { f ( x ) } { { ƒn ( x ) } dx = 1⁄2 G [ * dx = 2G [ * fn ( x ) dx Σετ fη ( α ) can be integrated term by term over the interval ( 0 , ∞ ) , ( T > 0 ) ( ii ) the series 00 Σ 2 ) f e- TM * ƒn ( x ) dx 0 is a ...
... transformation asserts G [ { f ( x ) } { { ƒn ( x ) } dx = 1⁄2 G [ * dx = 2G [ * fn ( x ) dx Σετ fη ( α ) can be integrated term by term over the interval ( 0 , ∞ ) , ( T > 0 ) ( ii ) the series 00 Σ 2 ) f e- TM * ƒn ( x ) dx 0 is a ...
الصفحة 18
... transformations really involve . In summing the series i \ 2 1+ a + a ( a + 1 ) + we had to use two repetitions of Borel's is in reality the equivalent of ( a ) e bari m process : г ( a ) e - bari Som hence e- dv 00 00 -- a e- " dv e ...
... transformations really involve . In summing the series i \ 2 1+ a + a ( a + 1 ) + we had to use two repetitions of Borel's is in reality the equivalent of ( a ) e bari m process : г ( a ) e - bari Som hence e- dv 00 00 -- a e- " dv e ...
الصفحة 20
... transformation do not appear to be so interesting as those of the transformation of § 2. I shall therefore not discuss its legitimacy in great detail . The most interesting case appears to be the following . 20 MR HARDY , FURTHER ...
... transformation do not appear to be so interesting as those of the transformation of § 2. I shall therefore not discuss its legitimacy in great detail . The most interesting case appears to be the following . 20 MR HARDY , FURTHER ...
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عبارات ومصطلحات مألوفة
a₁ absolutely convergent applied asymptotic B₁ bounded function bracket C₂ CAMBRIDGE concomitant consider continuous function convergent corresponding cos² curve denote differential coefficient differential equation dx² elastic equal expression factor finite follows formula ƒ x Hence impact infinite integrand irreducible k₁ Lebesgue integral Lemma linear monotone monotone function obtain operator oscillation P₁ plastic positive pressure prove R₁ reciprocant repeated integrals respect result s₁ satisfied sequence shew solution summable suppose symbols theorem theory transformation U₂ uniformly uniformly convergent unique limit upper V₁ values variables velocity W. H. Young w₁ zero α₁ ах дг ди др ду дх მყ
مقاطع مشهورة
الصفحة 280 - We know, however, that this integral is also equal to the sum of the residues at the poles of the integrand /
الصفحة 286 - The sum of the residues at the poles of the last factor, which occurs in (13.18) is therefore equal to minus the sum of the residues at the poles of the other factors.
الصفحة 358 - Since the modulus of a sum is not greater than the sum of the moduli...
الصفحة 96 - In support of such an hypothesis we may remark that as the crystalline grains are built up from their various centres, there will in general be a certain number of molecules to spare between their surfaces ; and these molecules will evidently be distributed in the spaces between the grains with relatively small density, ie, in such a fluid or serai-fluid condition, as would just account for the viscous reaction required.
الصفحة 140 - ... the same properties as the forms upon which they effectively operate, and that the forms which are invariant and the operators are properly to be regarded as one system of forms possessing the same properties.
الصفحة 312 - A geometrical progression is a series in which the ratio of any term to the preceding term is the same for all terms of the series.
الصفحة 126 - Plemelj's canonical form for the principal part of the solving function of an integral equation of the second kind in the neighbour hood of a pole.
الصفحة 48 - would prove independent of the length of the rods, provided the velocity and other conditions of the impact were kept unchanged. This was found to be the case, so that, by plotting duration of impact against length of rods, a straight line was obtained, whose slope gave the required value of the wave-velocity. * " On the Effects of Momentary Stresses in Metals,
الصفحة 348 - Rules for determining when the process of reversing the order of integration in a repeated integral is allowable.
الصفحة 100 - We are concerned here with the variation of integral forms, or more specially with their invariance, under the action of an operator which is an extension of the hydrodynamical operator in Enler's equations.