#powerseries — Public Fediverse posts
Live and recent posts from across the Fediverse tagged #powerseries, aggregated by home.social.
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📈 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! 🧠🔄
http://www.deaneyang.com//blog/blog/math/exponential-function/euler-formula/2025/05/29/ExponentialFunctions.html #PowerSeries #Humor #MathPhilosophy #DrowningInMath #HackerNews #ngated -
📈 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! 🧠🔄
http://www.deaneyang.com//blog/blog/math/exponential-function/euler-formula/2025/05/29/ExponentialFunctions.html #PowerSeries #Humor #MathPhilosophy #DrowningInMath #HackerNews #ngated -
📈 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! 🧠🔄
http://www.deaneyang.com//blog/blog/math/exponential-function/euler-formula/2025/05/29/ExponentialFunctions.html #PowerSeries #Humor #MathPhilosophy #DrowningInMath #HackerNews #ngated -
📈 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! 🧠🔄
http://www.deaneyang.com//blog/blog/math/exponential-function/euler-formula/2025/05/29/ExponentialFunctions.html #PowerSeries #Humor #MathPhilosophy #DrowningInMath #HackerNews #ngated -
Honor Unveils Power Lineup: Mid-Range Phones With Large 8,000mAh Batteries
#batterylife #honor #MidRangePhones #PowerSeries #smartphone
https://blazetrends.com/honor-unveils-power-lineup-mid-range-phones-with-large-8000mah-batteries/?fsp_sid=6638 -
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?
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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?
-
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?
-
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?
-
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?
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Two must reads for anyone serious about sequences, computing methodologies, and combinatorial algorithms.
S. Yurkevich, The art of algorithmic guessing in gfun,
https://doi.org/10.5206/mt.v2i1.14421B. T. Tabuguia, W. Koepf, On the Rep. of Non-Holonomic Univariate Power Series,
https://doi.org/10.5206/mt.v2i1.14315The 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
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Two must reads for anyone serious about sequences, computing methodologies, and combinatorial algorithms.
S. Yurkevich, The art of algorithmic guessing in gfun,
https://doi.org/10.5206/mt.v2i1.14421B. T. Tabuguia, W. Koepf, On the Rep. of Non-Holonomic Univariate Power Series,
https://doi.org/10.5206/mt.v2i1.14315The 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
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Two must reads for anyone serious about sequences, computing methodologies, and combinatorial algorithms.
S. Yurkevich, The art of algorithmic guessing in gfun,
https://doi.org/10.5206/mt.v2i1.14421B. T. Tabuguia, W. Koepf, On the Rep. of Non-Holonomic Univariate Power Series,
https://doi.org/10.5206/mt.v2i1.14315The 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
-
Two must reads for anyone serious about sequences, computing methodologies, and combinatorial algorithms.
S. Yurkevich, The art of algorithmic guessing in gfun,
https://doi.org/10.5206/mt.v2i1.14421B. T. Tabuguia, W. Koepf, On the Rep. of Non-Holonomic Univariate Power Series,
https://doi.org/10.5206/mt.v2i1.14315The 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