| Symbol |
Meaning |
Definition/Example |
| ζ(s) |
Riemann zeta function |
ζ(2)=6π2 |
| Γ(z) |
Gamma function (complex) |
Γ(z)=∫0∞tz−1e−tdt |
| B(x,y) |
Beta function |
B(x,y)=Γ(x+y)Γ(x)Γ(y) |
| ψ(x) |
Digamma function |
ψ(x)=Γ(x)Γ′(x) |
| Heaviside(x) |
Heaviside step |
H(x)={10x≥0x<0 |
| δ(x) |
Dirac delta function |
∫−∞∞δ(x)dx=1 |
| sinc(x) |
sinc function |
sinc(x)=xsinx |
| rect(x) |
Rectangular function |
rect(x)={10∣x∣≤1/2otherwise |
| σx,σy,σz |
Pauli matrices |
σx=(0110) |
| c |
Cardinality of the continuum |
∣R∣=c |
| ∑n∈S |
Sum over a set |
∑n∈Nn21 |
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31
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Gμν+Λgμν=c48πGTμν
v=v1v2⋮vn
维恩位移定律:黑体辐射峰值波长与温度的关系:
λmaxT=2.898×10−3 m⋅K
graph LR
subgraph "N型硅 (N_D=10^16 cm^-3)"
A[低温域 T<50K] -->|冻析效应| B[大部分施主未电离]
B --> C[n ≈ N_D/10]
D[室温 T=300K] -->|完全电离| E[n ≈ N_D]
F[高温 T>500K] -->|本征激发占主导| G[n ≈ n_i]
end
sequenceDiagram
autonumber
participant 1 as $$\alpha$$
participant 2 as $$\beta$$
1->>2: Solve: $$\sqrt{2+2}$$
2-->>1: Answer: $$2$$
Note right of 2: $$\sqrt{2+2}=\sqrt{4}=2$$