Entries from 2022-09-01 to 1 month

bone

bone ト sanus ハ、関係ガ有リ、bone ガ接着スレバ sanus ヲ害ス。 T.theodor 2022.9.30.

zeta function

ζ(s) = 1+1/2s−1−1/2sn(2s−1)+1/3s−1−1/33sn(3s−1)+… lim ζ(s) = 1+1/2s−1+1/3s−1+… T.theodor 2022.9.30.

blood flow

blood flow ト morbus ハ、関係ガ有リ、blood flow ニ支障ガ有レバ、morbus ヲ生ズ。 T.theodor 2022.9.29.

function

y = 1/xn+a+b asymptote y = ±1a±b x = ±1/a x>n√1/1+b−a y<1 x<n√1/1+b−a y>1 lim 1/xn+a+b = ±1a±b T.theodor 2022.9.29.</n√1/1+b−a>

function

y = 1/xn+a+b asymptote y = ±1a±b x = ±1/a x>n√1/1+b−a y<1 x<n√1/1+b−a y>1 lim 1/xn+a+b = ±1a±b T.theodor 2022.9.29.</n√1/1+b−a>

infinit series

1+1/3+1/6… = 2−2/n+1 T.theodor 2022.9.28.

infinite series

ak= (−1) n−1n = [n+1/2]([n+1/2]+1)−[n+1/2]−[n/2]([n/2]+1) T.theodor 2022.9.28.

natural logarithm

log(1+x) ≠ Σ(−1)n+1/nxn T.heodor 2022.9.27.

logical fallacy of Gaussian integral

exp −(x2 + y2) ≠ exp −r2 ≠ √π T.theodor 2022.9.27.

Infinite product

Π 1−1/ns T.theodor 2022.9.26.

function

f(x) = αxn+βxn-1…+ω g(x) = α'x+β' S = |α|/n(n+1) (b−a)n T.theodor 2022.9.27.

function

f(x) = αxn+βxn-1…+ω g(x) = α'x+β' S = |α|/n(n+1) (b−a)n T.theodor 2022.9.27.

logical fallacy of Stirling's approximation

n! ≠ 2.5√n(n/e)neλn e ≒ 2.71 T.theodor 2022.9.27.

logical fallacy of Stirling's approximation

n! ≠ 2.5√n(n/e)neλn e ≒ 2.71 T.theodor 2022.9.27.

logical fallacy of gamma function

Γ(n) ≠ n!,Γ(n) ≠ (n−1)! T.theodor 2022.9.27.

logical fallacy of Beta function

B(z1,z2) ≠ B(z2,z1) z1 = a+bi z2 = c+di f(x) = tz1 −1(1−t)z2 −1 T.theodor 2022.9.26.

logical fallacy of Beta function

B(z1,z2) ≠ B(z2,z1) z1 = a+bi z2 = c+di f(x) = tz1 −1(1−t)z2 −1 T.theodor 2022.9.26.

Infinite product

Π 1−1/ns T.theodor 2022.9.26.

logical fallacy of Functio zeta Riemanniana

(1−1/2s)ζ(s) = (1−1/2s)+… ζ(s) ≠ Πp 1/1−p-s T.theodor 2022.9.26.

n-th root

n≧3 1 < < 2k√x (2k

function

f(x) = αxn+βxn-1…+ω ω ≠ 2n f(1) ≠ 0 −2n < ω < 2n ω ≠ Z T.theodor 2022.9.25.

zeta function

ζ(x) = 1/xs s = 1 lim Σ ζ(x) = 3975/30241681512+0.15611… = 2.78507936508 T.theodor 2022.9.25.

logical fallacy of Euler's product formula

ζ(s) =1+1/2s+13s+… 1/2sζ(s) =1/2s+14s+… (1−1/2s)ζ(s) =1+1/3s+… (1−1/2s)(1−1/3s)ζ(s) =1+1/45s+… ・ ・ ζ(s) ≠ Π1/1−1/ps T.theodor 2022.9.30.

Three-dimensional space et sphere

Two-dimensional space,Three-dimensional space and circle,sphere ハ、異次元ヲ形成スル。 T.theodor 2022.9.24.

function

Δy/Δxf(x) > 1 f(x) > x Δy/Δxf(x) < 1 f(x) < x T.theodor 2022.9.24.

function

Δy/Δxf(x) > 1 f(x) > x Δy/Δxf(x) < 1 f(x) < x T.theodor 2022.9.24.

function

a/bx2+y2 = r2 T.theodor 2022.9.23.

function

a2/x2+b2/y2 = 1 T.theodor 2022.9.23.

Close-packing of equal spheres

radius = r L=4/√2r h → ∞ FCC(n) > HCP(n) T.theodor 2022.9.23.