?: sinc(0) = 1 (Първият Хилбертов проблем)
При себе си:
limt→0∫01cos(ωt)dω
||
limt→0[(1/t)sin(t)]
||
limt→0[1**sinc(t)] = 1**
↓
(d/dt)limt→0sinc(t) = 0
↕
(d/dt)[0dsin(t)/0dt] = 0
↕
∫(d/dt)[0dsin(t)/0dt]dt = ∫0dt
↕
0dsin(t)/0dt = const(ω) = const(0) = dt/dt
↕
||
limt→0[(1/t)sin(t)]
||
limt→0[1**sinc(t)] = 1**
↓
(d/dt)limt→0sinc(t) = 0
↕
(d/dt)[0dsin(t)/0dt] = 0
↕
∫(d/dt)[0dsin(t)/0dt]dt = ∫0dt
↕
0dsin(t)/0dt = const(ω) = const(0) = dt/dt
↕
| cos(t) = 1 ↔ t = 0
| sin(t) = t ↔ sinc(t) = 1
| sin(t) = t ↔ sinc(t) = 1
↕
sinc(0)
= 1
* Т. е. откъм умопостигаем, та къмто опитен характер (Ясперс)
** При мене си (?): ∫01cos(ωt)dω = (1/t)sin(t) = 1sinc(t) → (къмто себе си***)
*** Хайдегер или пък къмто мене си (Сартр)
P. S. W. Blake, "To Mrs. Ann Flaxman":
Its form was lovely, but its colours - pale;
One standing in the porches of the sun,
When his merid'an glories were begun,
Leaped from the steps of fire 'nd on the grass,
Alighted where this little flower was,
With hands divine he moved the gentle sod,
And took the flower up in 'ts native clod,
Then planting it upon a mountain's brow:
'Tis your own fault if you don't flourish now"
Допълнението към статията ми "Дяволите да ни вземат", pdf: link