Statements (20)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:defines |
A sequence of definite integrals involving products of sinc functions
|
| gptkbp:field |
gptkb:mathematics
|
| gptkbp:hasSubfield |
analysis
|
| https://www.w3.org/2000/01/rdf-schema#label |
Borwein integrals
|
| gptkbp:namedAfter |
gptkb:Peter_Borwein
gptkb:Jonathan_Borwein |
| gptkbp:notableExample |
∫₀^∞ (sin x / x)(sin(x/3)/(x/3))(sin(x/5)/(x/5)) dx = π/2
∫₀^∞ (sin x / x)(sin(x/3)/(x/3))...(sin(x/15)/(x/15)) dx ≠ π/2 ∫₀^∞ (sin x / x) dx = π/2 ∫₀^∞ (sin x / x)(sin(x/3)/(x/3)) dx = π/2 |
| gptkbp:notableFor |
The first few integrals in the sequence evaluate to π/2, but the pattern breaks at the eighth integral
|
| gptkbp:publishedIn |
gptkb:American_Mathematical_Monthly
|
| gptkbp:relatedTo |
Fourier analysis
integral calculus sinc function definite integral |
| gptkbp:studiedBy |
1980s
|
| gptkbp:bfsParent |
gptkb:Jonathan_M._Borwein
|
| gptkbp:bfsLayer |
6
|