The Messenger of Mathematics, Volumes 6-7Macmillan and Company, 1877 - Mathematics |
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... Formula leading to an Expression for E. By Professor Cayley On some Elliptic Function Identities . By J. W. L. Glaisher 28 102 2282 29 63 On an Application of Elliptic Functions to a Problem in the Distribution of Heat in a Rectangular ...
... Formula leading to an Expression for E. By Professor Cayley On some Elliptic Function Identities . By J. W. L. Glaisher 28 102 2282 29 63 On an Application of Elliptic Functions to a Problem in the Distribution of Heat in a Rectangular ...
Page 30
... formula ( 2 ) can be readily proved , for whence dve - ko2 - cos v ( a − x ) = 1 √√ ( 7 ) е ( a - x ) 2 4k dve ̄ko2 -8 = √ ( 7 ) م dap ( a ) [ * ( a - x ) 2 4k 18 cosv ( a - x ) = √√ ( 7 ) " _dae 4 * ̄p ( a ) √ (笑)」 22 dze 4k ...
... formula ( 2 ) can be readily proved , for whence dve - ko2 - cos v ( a − x ) = 1 √√ ( 7 ) е ( a - x ) 2 4k dve ̄ko2 -8 = √ ( 7 ) م dap ( a ) [ * ( a - x ) 2 4k 18 cosv ( a - x ) = √√ ( 7 ) " _dae 4 * ̄p ( a ) √ (笑)」 22 dze 4k ...
Page 49
... is readily deduced from the formula x2P2 - 2 ••• ± x " F1 = 0 , if n be uneven n.n- 1 P1- nxP + 11-1 1.2 3 5 n 1 = 6 ... n ( x2 - 1 ) " , if n be even , VOL . VI . E ( see Proceedings of the London Mathematical Society , vol ( 49 )
... is readily deduced from the formula x2P2 - 2 ••• ± x " F1 = 0 , if n be uneven n.n- 1 P1- nxP + 11-1 1.2 3 5 n 1 = 6 ... n ( x2 - 1 ) " , if n be even , VOL . VI . E ( see Proceedings of the London Mathematical Society , vol ( 49 )
Page 50
... , ... 1 , 1 , 1 , 1 , ... 31 21 1 1 1 , 1 , 3 , 4 , 3 ... = = & c . , ( n rows ) . x 19 86 - log ( 1 + x ) and that the coefficients in the quadratures formula are the 50 EXPRESSIONS FOR LAPLACE'S COEFFICIENTS , & c .
... , ... 1 , 1 , 1 , 1 , ... 31 21 1 1 1 , 1 , 3 , 4 , 3 ... = = & c . , ( n rows ) . x 19 86 - log ( 1 + x ) and that the coefficients in the quadratures formula are the 50 EXPRESSIONS FOR LAPLACE'S COEFFICIENTS , & c .
Page 51
and that the coefficients in the quadratures formula are the same , only all taken with the negative sign , viz . 1 17 h [ pxdx = ± pa + 4 ( a + h ) ... + 4 ( b − 1 ) + 1þð h ) - - 1 ΔΦ ( 6 – 1 ) - Αφα } - - - – 24 { △ 3p ( b − 2h ) ...
and that the coefficients in the quadratures formula are the same , only all taken with the negative sign , viz . 1 17 h [ pxdx = ± pa + 4 ( a + h ) ... + 4 ( b − 1 ) + 1þð h ) - - 1 ΔΦ ( 6 – 1 ) - Αφα } - - - – 24 { △ 3p ( b − 2h ) ...
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a₁ Algebra ALLEN WHITWORTH angle axis B₁ calculation CAMBRIDGE centre circle cloth conics continued fraction cose Crown 8vo cube root curve cylinder denote determine dx dx dx dy dy dz Edition ÉDOUARD LUCAS Elliptic Functions equal expression FELLOW OF ST formula fourth number geometrical given whenever sufficient H. J. S. Smith harmonic Hence infinite integral J. W. L. GLAISHER JOHN'S COLLEGE Laplace's MESSENGER OF MATHEMATICS Metcalfe Metcalfe and Son method motion obtained parallel partial differential equation PENDLEBURY plane plate Price-One Shilling prime Prof Professor Cayley radius respectively result ruled surfaces satisfied sequence sewed solution sphere spherical Spherical Harmonics square sufficient diagrams suppose surface tangent theorem Theory Treatise triangle variable vols whence zero
Popular passages
Page 145 - Aperçu historique sur l'origine et le développement des méthodes en Géométrie, particulièrement de celles qui se rapportent à la Géométrie moderne, suivi d'un Mémoire de Géométrie sur deux principes généraux de la Science, la Dualité et l'Homographie.
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Page 112 - Coll (communicated by Prof. Crofton, FRS) entitled "The Calculus of Equivalent Statements." A short account of this analytical method has been given in the July and November numbers (1877) of the Educational Times, under the name of Symbolical Language. The chief use at present made of it is to determine the new limits of integration •when we change the order of integration or the variables in a multiple integral, and also to determine the limits of integration in questions relating to probability.
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Page 152 - Rara Mathematica ; or a Collection of Treatises on the Mathematics and Subjects connected with them, from ancient inedited MSS. by JO HALLIWELL, 8vo.
Page 160 - The History of the Heavens, considered according to the notions of the Poets and Philosophers, compared with the Doctrines of Moses.
Page 160 - A letter to the Board of Visitors of the Greenwich Royal Observatory in reply to the calumnies of Mr. Babbage at their meeting in June 1853, and in his book entitled The Exposition of 1851.