Fix formula in notes; axial T-matrix WIP

Former-commit-id: a94506c8f40e20b425167bc56fd632cfde335a7a

notes/cylinderT.lyx

@@ -111,8 +111,8 @@ literal "false"
 :
 \begin_inset Formula 
 \begin{align*}
-R_{nn'} & =ik^{2}\iint_{S_{s}}\left(\frac{\eta}{\eta_{1}}\wfkcreg_{n}\left(k\vect r\right)\times\wfkcreg_{\overline{n'}}\left(k\vect r\right)+\wfkcreg_{\overline{n'}}\left(k\vect r\right)\times\wfkcreg_{n}\left(k\vect r\right)\right)\cdot\uvec{\nu}\,\ud S,\\
+R_{nn'} & =ik^{2}\iint_{S_{s}}\left(\frac{\eta}{\eta_{1}}\wfkcreg_{n}\left(k\vect r\right)\times\wfkcreg_{\overline{n'}}\left(k_{1}\vect r\right)+\wfkcreg_{\overline{n}}\left(k\vect r\right)\times\wfkcreg_{n'}\left(k_{1}\vect r\right)\right)\cdot\uvec{\nu}\,\ud S,\\
-Q_{nn'} & =ik^{2}\iint_{S_{s}}\left(\frac{\eta}{\eta_{1}}\wfkcout_{n}\left(k\vect r\right)\times\wfkcreg_{\overline{n'}}\left(k\vect r\right)+\wfkcout_{\overline{n'}}\left(k\vect r\right)\times\wfkcreg_{n}\left(k\vect r\right)\right)\cdot\uvec{\nu}\,\ud S,
+Q_{nn'} & =ik^{2}\iint_{S_{s}}\left(\frac{\eta}{\eta_{1}}\wfkcout_{n}\left(k\vect r\right)\times\wfkcreg_{\overline{n'}}\left(k_{1}\vect r\right)+\wfkcout_{\overline{n}}\left(k\vect r\right)\times\wfkcreg_{n'}\left(k_{1}\vect r\right)\right)\cdot\uvec{\nu}\,\ud S,
 \end{align*}
 
 \end_inset
@@ -121,11 +121,15 @@ where
 \begin_inset Formula $S_{s}$
 \end_inset
 
- is the scatterer surface and 
+ is the scatterer surface, 
 \begin_inset Formula $\uvec{\nu}$
 \end_inset
 
- is the outwards pointing unit normal to it; then
+ is the outwards pointing unit normal to it, and the subscript
+\begin_inset Formula $_{1}$
+\end_inset
+
+ refers to the particle inside; then
 \begin_inset Formula 
 \[
 T_{nn'}=-\sum_{n''}R_{nn''}Q_{n''n}^{-1}.

qpms/tmatrices.c

@@ -609,7 +609,24 @@ qpms_arc_function_retval_t qpms_arc_cylinder(double theta, const void *param) {
   return res;
 }
 
+
+struct tmatrix_axialsym_integral_param_t {
+  const qpms_vswf_set_spec_t *bspec;
+  qpms_l_t l1, l2; 
+  qpms_m_t m1; // m2 = -m1
+  qpms_vswf_type_t t1; // t2 = 2 - t1
+  qpms_arc_function_t f;
+  complex double k_in, k, z_in, z;
+  bool realpart; // Otherwise imaginary part
+  bool Q; // Otherwise R
+};
+
 #if 0
+static double tmatrix_axialsym_integrand(double theta, void *param) {
+  struct tmatrix_axialsym_integral_param_t *p = param;
+
+}
+
 qpms_errno_t qpms_tmatrix_axialsym_fill(
 		qpms_tmatrix_t *t, complex double omega, qpms_epsmu_generator_t outside,
 		qpms_epsmu_generator_t inside,qpms_arc_function_t shape)