docs: fix unrendered LaTeX math blocks in indicator docs

Blank lines were missing around $$ fences (bold labels or list items
glued directly to $$, and stacked $$ blocks with no separator),
causing GitHub to merge them into the surrounding paragraph and
misread underscores as italic markers instead of rendering math.

lib/filters/cheby1/Cheby1.md

@@ -40,16 +40,21 @@ $$
 2. **Pre-warped Frequency**: $W_c = \tan(\frac{\omega_c}{2})$
 3. **Ripple Factor**: $\epsilon = \sqrt{10^{R/10} - 1}$
 4. **Transformation**:
+
     $$
     \mu = \frac{1}{2} \sinh^{-1}(\frac{1}{\epsilon}) \\
     \sigma = -\sinh(\mu) W_c \\
     \omega_d = \cosh(\mu) W_c
     $$
+
 5. **Intermediate Variables**:
+
     $$
     K = \sigma^2 + \omega_d^2
     $$
+
 6. **S-Plane to Z-Plane Map (Bilinear Transform)**:
+
     $$
     b_0' = K \\
     b_1' = 2K \\
@@ -58,7 +63,9 @@ $$
     a_1' = 2K - 2 \\
     a_2' = 1 + 2\sigma + K
     $$
+
 7. **Coefficients**:
+
     $$
     b_0 = \frac{b_0'}{a_0'}, \quad b_1 = \frac{b_1'}{a_0'}, \quad b_2 = \frac{b_2'}{a_0'} \\
     a_1 = \frac{a_1'}{a_0'}, \quad a_2 = \frac{a_2'}{a_0'}

lib/filters/tbf/Tbf.md

@@ -63,11 +63,13 @@ This is an IIR filter - each output depends on all previous outputs, creating in
 The truncated version limits memory to exactly $L$ bars by recomputing the IIR recursion from scratch each bar:
 
 **Step 1:** Initialize the tail:
+
 $$
 T_{L+2} = 0, \qquad T_{L+1} = 0
 $$
 
 **Step 2:** Run the recursion forward from oldest to newest:
+
 $$
 T_k = a_0(P_{k-1} - P_{k+1}) + a_1 \cdot T_{k+1} + a_2 \cdot T_{k+2}, \qquad k = L, L{-}1, \ldots, 1
 $$
@@ -75,6 +77,7 @@ $$
 where $P_k$ denotes the close price $k$ bars ago.
 
 **Step 3:** Output:
+
 $$
 \text{TBF}_t = T_1
 $$

lib/forecasts/afirma/Afirma.md

@@ -76,21 +76,25 @@ where $x$ is the input series and $w_k$ are the window weights.
 ### Window Coefficient Formulas
 
 **Hanning:**
+
 $$
 w_k = 0.5 - 0.5 \cos\left(\frac{2\pi k}{P}\right)
 $$
 
 **Hamming:**
+
 $$
 w_k = 0.54 - 0.46 \cos\left(\frac{2\pi k}{P}\right)
 $$
 
 **Blackman:**
+
 $$
 w_k = 0.42 - 0.5 \cos\left(\frac{2\pi k}{P}\right) + 0.08 \cos\left(\frac{4\pi k}{P}\right)
 $$
 
 **Blackman-Harris:**
+
 $$
 w_k = 0.35875 - 0.48829 \cos\left(\frac{2\pi k}{P}\right) + 0.14128 \cos\left(\frac{4\pi k}{P}\right) - 0.01168 \cos\left(\frac{6\pi k}{P}\right)
 $$
@@ -118,6 +122,7 @@ $$
 Fitted value at lag $i$: $\hat{x}_i = \text{intercept} + \text{slope} \cdot i$
 
 Final LS output:
+
 $$
 \text{AFIRMA}_{LS} = \frac{1}{P} \left( \sum_{i=0}^{n-1} \hat{x}_i + \sum_{i=n}^{P-1} x_{t-i} \right)
 $$

lib/numerics/logtrans/Logtrans.md

@@ -35,16 +35,19 @@ Key identities:
 ### Logarithm Rules
 
 **Product Rule:**
+
 $$
 \ln(a \cdot b) = \ln(a) + \ln(b)
 $$
 
 **Quotient Rule:**
+
 $$
 \ln\left(\frac{a}{b}\right) = \ln(a) - \ln(b)
 $$
 
 **Power Rule:**
+
 $$
 \ln(a^n) = n \cdot \ln(a)
 $$

lib/volatility/adr/Adr.md

@@ -78,16 +78,19 @@ $$
 Where $MA$ is one of:
 
 **SMA:**
+
 $$
 ADR_t = \frac{1}{N} \sum_{i=0}^{N-1} DR_{t-i}
 $$
 
 **EMA:**
+
 $$
 ADR_t = \alpha \cdot DR_t + (1 - \alpha) \cdot ADR_{t-1}, \quad \alpha = \frac{2}{N+1}
 $$
 
 **WMA:**
+
 $$
 ADR_t = \frac{\sum_{i=0}^{N-1} (N-i) \cdot DR_{t-i}}{\sum_{i=0}^{N-1} (N-i)}
 $$

lib/volatility/bbwp/Bbwp.md

@@ -63,6 +63,7 @@ $$
 $$
 
 Using Welford's running algorithm:
+
 $$
 \sigma = \sqrt{\frac{\sum x^2}{n} - \left(\frac{\sum x}{n}\right)^2}
 $$
@@ -70,6 +71,7 @@ $$
 ### Percentile Rank Formula
 
 For a value $v$ in a dataset of $N$ values:
+
 $$
 \text{Percentile} = \frac{\text{count of values} < v}{N}
 $$

lib/volatility/jvolty/Jvolty.md

@@ -79,6 +79,7 @@ This smoothed deviation represents the "raw" volatility reading that feeds into
 The core innovation: instead of exponential smoothing, JVOLTY maintains a 128-sample circular buffer of raw volatility readings. On each bar, the buffer is sorted and a trimmed mean is computed:
 
 **Full buffer (128 samples):**
+
 $$
 \hat{V}_t = \frac{1}{65} \sum_{i=32}^{96} \text{sorted}[i]
 $$
@@ -86,12 +87,15 @@ $$
 The middle 65 values (indices 32-96) represent approximately the 25th-75th percentile. Extreme values on both tails are discarded.
 
 **Partial buffer (16-127 samples):**
+
 $$
 s = \max(5, \text{round}(0.5 \times \text{count}))
 $$
+
 $$
 k = \lfloor(\text{count} - s) / 2\rfloor
 $$
+
 $$
 \hat{V}_t = \frac{1}{s} \sum_{i=k}^{k+s-1} \text{sorted}[i]
 $$
@@ -133,6 +137,7 @@ $$
 $$
 
 where:
+
 $$
 \text{sqrtDivider} = \frac{\sqrt{L} \times \text{logParam}}{\sqrt{L} \times \text{logParam} + 1}
 $$

lib/volatility/natr/Natr.md

@@ -81,6 +81,7 @@ Given period $N$:
 1. **Parameters**: $\alpha = \frac{1}{N}$, $\text{decay} = 1 - \alpha$
 
 2. **True Range**:
+
 $$
 TR_t = \begin{cases}
 H_t - L_t & \text{if } t = 0 \\
@@ -89,16 +90,19 @@ H_t - L_t & \text{if } t = 0 \\
 $$
 
 3. **RMA with FMA optimization**:
+
 $$
 ATR_{raw,t} = \text{FMA}(ATR_{raw,t-1}, \text{decay}, \alpha \cdot TR_t)
 $$
 
 4. **Warmup compensation**:
+
 $$
 ATR_t = \frac{ATR_{raw,t}}{1 - e_t}
 $$
 
 5. **Normalization**:
+
 $$
 NATR_t = \frac{ATR_t}{C_t} \times 100
 $$

lib/volatility/vr/Vr.md

@@ -57,11 +57,13 @@ $$
 where $\alpha = 1/\text{period}$.
 
 **Bias compensator:**
+
 $$
 e_t = (1 - \alpha)^t
 $$
 
 **Corrected ATR:**
+
 $$
 ATR_t = \frac{\text{RMA}_{raw,t}}{1 - e_t}
 $$

lib/volatility/yzv/Yzv.md

@@ -67,16 +67,19 @@ where $n$ is the smoothing period. For typical values:
 ### 3. Daily Variance Components
 
 **Overnight variance:**
+
 $$
 \sigma_o^2 = r_o^2
 $$
 
 **Open-to-close variance:**
+
 $$
 \sigma_c^2 = r_c^2
 $$
 
 **Rogers-Satchell variance (drift-independent intraday measure):**
+
 $$
 \sigma_{RS}^2 = r_h \cdot (r_h - r_c) + r_l \cdot (r_l - r_c)
 $$
@@ -108,11 +111,13 @@ $$
 where $\alpha = 1/n$.
 
 **Bias compensator:**
+
 $$
 e_t = (1 - \alpha)^t
 $$
 
 **Corrected output:**
+
 $$
 \text{RMA}_{corrected} = \frac{\text{RMA}_{raw}}{1 - e_t}
 $$
@@ -127,6 +132,7 @@ The Rogers-Satchell component has elegant properties:
 - **Non-negativity**: Always ≥ 0 when calculated correctly
 
 The formula $r_h(r_h - r_c) + r_l(r_l - r_c)$ can be rewritten as:
+
 $$
 \sigma_{RS}^2 = r_h \cdot r_l - r_l \cdot r_c - r_h \cdot r_c + r_h^2 + r_l^2 - r_l^2
 $$

lib/volume/efi/Efi.md

@@ -83,11 +83,13 @@ where:
 ### Smoothed Force Index
 
 Standard EMA form:
+
 $$
 EFI_t = \alpha \times F_t + (1 - \alpha) \times EFI_{t-1}
 $$
 
 Using FMA optimization:
+
 $$
 EFI_t = \text{FMA}(\alpha, F_t - EFI_{t-1}, EFI_{t-1})
 $$

lib/volume/vroc/Vroc.md

@@ -39,11 +39,13 @@ $$
 ### 2. Rate of Change Calculation
 
 **Percentage Mode** (default):
+
 $$
 \text{VROC}_t = \frac{V_t - V_{t-n}}{V_{t-n}} \times 100
 $$
 
 **Point Mode**:
+
 $$
 \text{VROC}_t = V_t - V_{t-n}
 $$