"Taylor polynomial" meaning in All languages combined

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      "examples": [
        {
          "ref": "1980, Donald W. Kahn, Introduction to Global Analysis, Academic Press, page 314",
          "text": "For example, if Mⁿ#x3D;#x5C;mathbb#x7B;R#x7D;ⁿ and Nᵏ#x3D;#x5C;mathbb#x7B;R#x7D;, a singularity means the vanishing of the gradient, or equivalently, the linear terms of the Taylor's polynomial of some degree greater than 1. If one has a singularity, one may look at the second-order terms in the Taylor's polynomial.",
          "type": "quotation"
        },
        {
          "ref": "1989, J. Berry, John Stephen Berry, A. Norcliffe, S. Humble, Introductory Mathematics Through Science Applications, Cambridge University Press, page 211",
          "text": "The polynomial approximation above for exp(x) is an example of a Taylor polynomial of degree 2 and in fact the polynomial approximations to sin(x) and cos(x) that we wrote down in Chapter 3 are also Taylor polynomials.",
          "type": "quotation"
        },
        {
          "ref": "2007, Andrea Bonfiglioli, Ermanno Lanconelli, Francesco Uguzzoni, Stratified Lie Groups and Potential Theory for their Sub-Laplacians, Springer, page 733",
          "text": "Then, we introduce and investigate the Taylor polynomials and we prove suitable versions of the Lagrange mean value theorem and of the Taylor formula.",
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      "glosses": [
        "A truncated Taylor series; the sum of the first n terms of a Taylor series."
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        "(mathematical analysis) A truncated Taylor series; the sum of the first n terms of a Taylor series."
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          "word": "Maclaurin polynomial"
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          "word": "Taylor's polynomial"
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          "code": "da",
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          "sense": "truncated Taylor series",
          "word": "Taylorpolynomium"
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  "word": "Taylor polynomial"
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          "ref": "1980, Donald W. Kahn, Introduction to Global Analysis, Academic Press, page 314",
          "text": "For example, if Mⁿ#x3D;#x5C;mathbb#x7B;R#x7D;ⁿ and Nᵏ#x3D;#x5C;mathbb#x7B;R#x7D;, a singularity means the vanishing of the gradient, or equivalently, the linear terms of the Taylor's polynomial of some degree greater than 1. If one has a singularity, one may look at the second-order terms in the Taylor's polynomial.",
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        },
        {
          "ref": "1989, J. Berry, John Stephen Berry, A. Norcliffe, S. Humble, Introductory Mathematics Through Science Applications, Cambridge University Press, page 211",
          "text": "The polynomial approximation above for exp(x) is an example of a Taylor polynomial of degree 2 and in fact the polynomial approximations to sin(x) and cos(x) that we wrote down in Chapter 3 are also Taylor polynomials.",
          "type": "quotation"
        },
        {
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          "text": "Then, we introduce and investigate the Taylor polynomials and we prove suitable versions of the Lagrange mean value theorem and of the Taylor formula.",
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        "A truncated Taylor series; the sum of the first n terms of a Taylor series."
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        "(mathematical analysis) A truncated Taylor series; the sum of the first n terms of a Taylor series."
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  "synonyms": [
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  "translations": [
    {
      "code": "da",
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      "sense": "truncated Taylor series",
      "word": "Taylorpolynomium"
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  ],
  "word": "Taylor polynomial"
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