planck_dIdT

 dIdT=planck_dIdT(nu,T)

 Partial derivative of the Planck function with respect
 to temperature at given temperature and frequency.

 Input in Hz and K
 Output in W m^-2 Hz^-1 ster^-1 K^-1

 eg: To reproduce the plot Carlstrom uses everywhere:

 nu=0:1e9:500e9; Tcmb=2.726; y=1e-4;
 fx=sz_fx(nu); delTsz=Tcmb.*fx*y;
 dIdT=planck_dIdT(nu,Tcmb);
 delIsz=delTsz.*dIdT; plot(nu,delIsz.*1e7*1e-4);

0001 function dIdT=planck_dIdT(nu,T)
0002 % dIdT=planck_dIdT(nu,T)
0003 %
0004 % Partial derivative of the Planck function with respect
0005 % to temperature at given temperature and frequency.
0006 %
0007 % Input in Hz and K
0008 % Output in W m^-2 Hz^-1 ster^-1 K^-1
0009 %
0010 % eg: To reproduce the plot Carlstrom uses everywhere:
0011 %
0012 % nu=0:1e9:500e9; Tcmb=2.726; y=1e-4;
0013 % fx=sz_fx(nu); delTsz=Tcmb.*fx*y;
0014 % dIdT=planck_dIdT(nu,Tcmb);
0015 % delIsz=delTsz.*dIdT; plot(nu,delIsz.*1e7*1e-4);
0016 
0017 h=6.626e-34;
0018 k=1.38e-23;
0019 c=3e8;
0020 x=(h*nu)./(k*T);
0021 
0022 dIdT=((2*h^2*nu.^4)./(c^2*k*T.^2)).*(exp(x)./(exp(x)-1).^2);