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#powerseries — Public Fediverse posts

Live and recent posts from across the Fediverse tagged #powerseries, aggregated by home.social.

  1. 📈 So you thought you could dodge #calculus with a “conceptual” take on Euler's formula? 😂 Spoiler: it's just a fancy way to say you're still drowning in power series, but now with extra philosophy! 🧠🔄
    deaneyang.com//blog/blog/math/ #PowerSeries #Humor #MathPhilosophy #DrowningInMath #HackerNews #ngated

  2. 📈 So you thought you could dodge #calculus with a “conceptual” take on Euler's formula? 😂 Spoiler: it's just a fancy way to say you're still drowning in power series, but now with extra philosophy! 🧠🔄
    deaneyang.com//blog/blog/math/ #PowerSeries #Humor #MathPhilosophy #DrowningInMath #HackerNews #ngated

  3. 📈 So you thought you could dodge #calculus with a “conceptual” take on Euler's formula? 😂 Spoiler: it's just a fancy way to say you're still drowning in power series, but now with extra philosophy! 🧠🔄
    deaneyang.com//blog/blog/math/ #PowerSeries #Humor #MathPhilosophy #DrowningInMath #HackerNews #ngated

  4. 📈 So you thought you could dodge #calculus with a “conceptual” take on Euler's formula? 😂 Spoiler: it's just a fancy way to say you're still drowning in power series, but now with extra philosophy! 🧠🔄
    deaneyang.com//blog/blog/math/ #PowerSeries #Humor #MathPhilosophy #DrowningInMath #HackerNews #ngated

  5. The integral

    \[ \int_0^\infty x^k e^{-x} dx = k! \]

    is used as motivation for the gamma function and in the irrationality proof of \( e \). But it can also be used for the transformation \( T \) defined by

    \[ T f = \int_0^\infty f(x) e^{-x} dx. \]

    If \( f = \sum_i f_i x^i \) is a power series and everything converges, it is transformed to \( T f = \sum_i f_i i! \). One can therefore say that \( T \) evaluates \( f \) at the factorial and write

    \[ T f = f(!). \]

    Are there other unusual places at which one can evaluate a function?

    #Mathematics #PowerSeries #Integrals

  6. The integral

    \[ \int_0^\infty x^k e^{-x} dx = k! \]

    is used as motivation for the gamma function and in the irrationality proof of \( e \). But it can also be used for the transformation \( T \) defined by

    \[ T f = \int_0^\infty f(x) e^{-x} dx. \]

    If \( f = \sum_i f_i x^i \) is a power series and everything converges, it is transformed to \( T f = \sum_i f_i i! \). One can therefore say that \( T \) evaluates \( f \) at the factorial and write

    \[ T f = f(!). \]

    Are there other unusual places at which one can evaluate a function?

    #Mathematics #PowerSeries #Integrals

  7. The integral

    \[ \int_0^\infty x^k e^{-x} dx = k! \]

    is used as motivation for the gamma function and in the irrationality proof of \( e \). But it can also be used for the transformation \( T \) defined by

    \[ T f = \int_0^\infty f(x) e^{-x} dx. \]

    If \( f = \sum_i f_i x^i \) is a power series and everything converges, it is transformed to \( T f = \sum_i f_i i! \). One can therefore say that \( T \) evaluates \( f \) at the factorial and write

    \[ T f = f(!). \]

    Are there other unusual places at which one can evaluate a function?

    #Mathematics #PowerSeries #Integrals

  8. The integral

    \[ \int_0^\infty x^k e^{-x} dx = k! \]

    is used as motivation for the gamma function and in the irrationality proof of \( e \). But it can also be used for the transformation \( T \) defined by

    \[ T f = \int_0^\infty f(x) e^{-x} dx. \]

    If \( f = \sum_i f_i x^i \) is a power series and everything converges, it is transformed to \( T f = \sum_i f_i i! \). One can therefore say that \( T \) evaluates \( f \) at the factorial and write

    \[ T f = f(!). \]

    Are there other unusual places at which one can evaluate a function?

    #Mathematics #PowerSeries #Integrals

  9. The integral

    \[ \int_0^\infty x^k e^{-x} dx = k! \]

    is used as motivation for the gamma function and in the irrationality proof of \( e \). But it can also be used for the transformation \( T \) defined by

    \[ T f = \int_0^\infty f(x) e^{-x} dx. \]

    If \( f = \sum_i f_i x^i \) is a power series and everything converges, it is transformed to \( T f = \sum_i f_i i! \). One can therefore say that \( T \) evaluates \( f \) at the factorial and write

    \[ T f = f(!). \]

    Are there other unusual places at which one can evaluate a function?

    #Mathematics #PowerSeries #Integrals

  10. Two must reads for anyone serious about sequences, computing methodologies, and combinatorial algorithms.

    S. Yurkevich, The art of algorithmic guessing in gfun,
    doi.org/10.5206/mt.v2i1.14421

    B. T. Tabuguia, W. Koepf, On the Rep. of Non-Holonomic Univariate Power Series,
    doi.org/10.5206/mt.v2i1.14315

    The examples are primarily aimed at Maple users but the expositions are general enough to give a good start.

    #TheArtOfGuessing, #P-recursive sequences, #D-finite functions, #Holonomic, #PowerSeries

  11. Two must reads for anyone serious about sequences, computing methodologies, and combinatorial algorithms.

    S. Yurkevich, The art of algorithmic guessing in gfun,
    doi.org/10.5206/mt.v2i1.14421

    B. T. Tabuguia, W. Koepf, On the Rep. of Non-Holonomic Univariate Power Series,
    doi.org/10.5206/mt.v2i1.14315

    The examples are primarily aimed at Maple users but the expositions are general enough to give a good start.

    #TheArtOfGuessing, #P-recursive sequences, #D-finite functions, #Holonomic, #PowerSeries

  12. Two must reads for anyone serious about sequences, computing methodologies, and combinatorial algorithms.

    S. Yurkevich, The art of algorithmic guessing in gfun,
    doi.org/10.5206/mt.v2i1.14421

    B. T. Tabuguia, W. Koepf, On the Rep. of Non-Holonomic Univariate Power Series,
    doi.org/10.5206/mt.v2i1.14315

    The examples are primarily aimed at Maple users but the expositions are general enough to give a good start.

    #TheArtOfGuessing, #P-recursive sequences, #D-finite functions, #Holonomic, #PowerSeries

  13. Two must reads for anyone serious about sequences, computing methodologies, and combinatorial algorithms.

    S. Yurkevich, The art of algorithmic guessing in gfun,
    doi.org/10.5206/mt.v2i1.14421

    B. T. Tabuguia, W. Koepf, On the Rep. of Non-Holonomic Univariate Power Series,
    doi.org/10.5206/mt.v2i1.14315

    The examples are primarily aimed at Maple users but the expositions are general enough to give a good start.

    #TheArtOfGuessing, #P-recursive sequences, #D-finite functions, #Holonomic, #PowerSeries