Pustam | पुस्तम | পুস্তম🇳🇵<p>“A mathematician, like a painter or poet, is a maker of patterns. If his patterns are more permanent than theirs; it is because they are made with ideas.”<br />― G.H. Hardy, A Mathematician&#39;s Apology</p><p>Let&#39;s define something...<br />Difference transform<br />\[\boxed{\boxed{\mathcal{D}\{f\}(a,b):=\int_a^b\left(f(\lfloor x\rfloor)-f(x)\right)\ \mathrm{d}x}}\]</p><p>Here an operator \(\mathcal{D}\) is acting on a function \(f\), describing the difference between an indiscrete sum and a discrete sum on a certain interval \(a\) to \(b\). This operator may play a pivotal role in asymptotic expansions, analytic continuation, etc.</p><p><a href="https://mathstodon.xyz/tags/DifferenceTransform" class="mention hashtag" rel="tag">#<span>DifferenceTransform</span></a> <a href="https://mathstodon.xyz/tags/DifferenceTransformOperator" class="mention hashtag" rel="tag">#<span>DifferenceTransformOperator</span></a> <a href="https://mathstodon.xyz/tags/TranformOperator" class="mention hashtag" rel="tag">#<span>TranformOperator</span></a> <a href="https://mathstodon.xyz/tags/DifferenceTransformation" class="mention hashtag" rel="tag">#<span>DifferenceTransformation</span></a> <a href="https://mathstodon.xyz/tags/AsymptoticExpansion" class="mention hashtag" rel="tag">#<span>AsymptoticExpansion</span></a> <a href="https://mathstodon.xyz/tags/AnalyticContinuation" class="mention hashtag" rel="tag">#<span>AnalyticContinuation</span></a> <a href="https://mathstodon.xyz/tags/Mathematics" class="mention hashtag" rel="tag">#<span>Mathematics</span></a> <a href="https://mathstodon.xyz/tags/GHHardy" class="mention hashtag" rel="tag">#<span>GHHardy</span></a> <a href="https://mathstodon.xyz/tags/Mathematicians" class="mention hashtag" rel="tag">#<span>Mathematicians</span></a> <a href="https://mathstodon.xyz/tags/Definition" class="mention hashtag" rel="tag">#<span>Definition</span></a> <a href="https://mathstodon.xyz/tags/Prologue" class="mention hashtag" rel="tag">#<span>Prologue</span></a> <a href="https://mathstodon.xyz/tags/Maths" class="mention hashtag" rel="tag">#<span>Maths</span></a> <a href="https://mathstodon.xyz/tags/Poet" class="mention hashtag" rel="tag">#<span>Poet</span></a> <a href="https://mathstodon.xyz/tags/Painter" class="mention hashtag" rel="tag">#<span>Painter</span></a> <a href="https://mathstodon.xyz/tags/Patterns" class="mention hashtag" rel="tag">#<span>Patterns</span></a> <a href="https://mathstodon.xyz/tags/Beauty" class="mention hashtag" rel="tag">#<span>Beauty</span></a> <a href="https://mathstodon.xyz/tags/BeautyOfPatterns" class="mention hashtag" rel="tag">#<span>BeautyOfPatterns</span></a></p>