| Strong/weak limits and strong/weak differentials of multi-variable indeterminate forms. III: Transformations |
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| 作者姓名： | 宋光世 |
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| 作者单位： | Chongqing University，Chongqing 400030，P.R. China |
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| 摘 要： | 1SimplificationinsphericalcoordinatesInthesphericalcoordinatessystem,??y?x=rsinθcosφ,z=rsinθsinφ,=rcosθ,???00≤θ<π,≤θ<2π.Setk=?tanφ,yandK=?zcotθ,then,xxcosφcotθu=r0K(t,t')istransformedintor=r0K(tanφ,cos),φandis,whenφ=0,simplifiedintoatruncatedcurver=r°K(0,cotθ).Thelatteriseasiertoberesolvedandcanreverttotheformerthroughturningaroundfor180°.Example.Thereexistsu=z2=(rcosθ)2x2+y2+z2r2=r°cos2θ?φ°,0≤θ≤π,0≤φ<2π.AsshowninFig.1,XX′isthediameteroftheunitcircle,OP0i…
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Strong/weak limits and strong/weak differentials of multi-variable indeterminate forms. III: Transformations |
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| SONG Guang-shi Chongqing University,Chongqing ,P.R. China.Strong/weak limits and strong/weak differentials of multi-variable indeterminate forms. III: Transformations[J].Journal of Chongqing University,2004(2). |
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| Authors: | SONG Guang-shi Chongqing University Chongqing PR China |
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| Institution: | SONG Guang-shi Chongqing University,Chongqing 400030,P.R. China |
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| Abstract: | Various transforms of the indeterminate forms are presented in this part, which include simplification in spherical coordinates, origin translation, axis alteration, transformation of limit conservation and application of Xh?K0. Fundamental factors for numerical simplification are provided respectively for bi-variable indeterminate forms, tri-variable indeterminate forms and the universal extending multiplier. |
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| Keywords: | spherical coordinate indeterminate form multi-variable special form limit conservation transform |
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