Dear colleague, We have recently written up a paper entitled "RELATIVISTIC THERMAL BREMSSTRAHLUNG GAUNT FACTOR FOR THE INTRACLUSTER PLASMA. III. FREQUENCY INTEGRATED EMISSIVITY" and submitted it to The Astrophysical Journal. We have also uploaded it in astro-ph/0011044. We have completed a subroutine for the analytic fitting formulae reported in this paper and we would like to send it to you. We would most like to appreciate whatever comment you might have on our paper. With my best wishes, Naoki Itoh Department of Physics, Sophia University 7-1, Kioi-cho, Chiyoda-ku, Tokyo 102-8554 Japan Telephone 81 (0)3 3238 3431 Telefax 81 (0)3 3238 3341 cccccccccccccccccccccccccccccccccccccccccccccccccccccccc c the fitting formula of R.E.integrated Gaunt factor c c z = zi , ti =log10(t) c c z: atomic number c c t = temperature of intracluster plasma c c 1<=z<28 ,t = 10^6-10^8.5[K] c cccccccccccccccccccccccccccccccccccccccccccccccccccccccc implicit real*8(a-z) real*8 a(121) data a/1.40092D+00,-1.00893D-01,-2.40128D-03,6.27343D-02, *-9.06484D-02,9.79512D-03,4.41703D-02,1.23203D-01,-1.58523D-01, *-4.10980D-02,6.81836D-02,1.54638D-01,1.58466D-01,-2.25452D-01, *1.90501D-01,-9.96615D-02,-4.34963D-02,7.85887D-02,3.35024D-02, *3.03478D-02,-1.73758D-01,9.49741D-02,-1.23959D-01,2.46348D-01, *-1.00552D-01,-2.32050D-01,4.23102D-01,2.84554D-01,-5.65980D-01, *-1.09511D+00,1.19685D+00,7.58040D-01,-7.80917D-01,-1.16975D-01, *-2.86550D-02,2.16833D-01,-2.37181D-01,2.43977D-01,-2.53216D-01, *-8.74859D-02,7.33247D-01,-5.57371D-01,-2.36066D-01,2.65356D-01, *2.14395D-02,-2.24939D-01,3.13853D-02,3.66311D-01,-3.11848D-01, *-5.57177D-01,8.92841D-01,1.05388D+00,-1.54700D+00,-6.52591D-01, *8.72583D-01,2.34238D-02,2.62997D-02,1.08847D-01,8.57778D-02, *-7.75490D-01,-7.76022D-01,1.89781D+00,1.63143D+00,-2.48868D+00, *-9.86901D-01,1.25501D+00,-5.89208D-02,1.93223D-01,5.05110D-01, *-1.02700D+00,7.70985D-03,2.01951D+00,-2.76644D+00,-1.38406D+00, *3.74683D+00,2.07710D-01,-1.40357D+00,3.92687D-02,-1.74988D-01, *-2.81975D-01,2.46117D-01,7.80591D-01,1.60661D+00,-2.75074D+00, *-3.84191D+00,4.67373D+00,2.16066D+00,-2.48054D+00,1.06170D-01, *-2.47926D-01,-7.95224D-01,1.39771D+00,2.70056D-01,-2.26472D+00, *2.75232D+00,6.90910D-01,-3.33774D+00,4.09320D-01,9.72879D-01, *-1.47162D-02,1.20553D-01,1.14518D-01,-1.87375D-01,-3.03752D-01, *-7.94442D-01,1.34593D+00,1.94313D+00,-2.39266D+00,-1.07379D+00, *1.26406D+00,-4.37176D-02,1.36623D-01,3.42773D-01,-6.23280D-01, *-2.05378D-01,7.62416D-01,-6.86149D-01,1.00617D-01,6.80864D-01, *-3.66206D-01,-7.12021D-02/ ccccccccccccccccccccccccccccccccccccccccccccc c Here users determine. c ccccccccccccccccccccccccccccccccccccccccccccc zi1 = 1.d0 zi2 = 28.d0 ti1 = 6.d0 ti2 = 8.5d0 td =0.1d0 ccc do 1 zi = zi1,zi2 do 2 ti = ti1,ti2,td z = ( zi - 14.5d0)/13.5d0 t = ( ti - 7.25d0 )/1.25d0 ingco = A(1) +A(2)*z +A(3)*z**2 +A(4)*z**3 +A(5)*z**4 * +A(6)*z**5+A(7)*z**6 +A(8)*z**7 +A(9)*z**8 * +A(10)*z**9 +A(11)*z**10 * +( A(12)+A(13)*z+A(14)*z**2+A(15)*z**3+A(16)*z**4 * +A(17)*z**5+A(18)*z**6+A(19)*z**7 +A(20)*z**8 * +A(21)*z**9 +A(22)*z**10 )*T * +( A(23)+A(24)*z+A(25)*z**2+A(26)*z**3+A(27)*z**4 * +A(28)*z**5+A(29)*z**6+A(30)*z**7 +A(31)*z**8 * +A(32)*z**9 +A(33)*z**10 )*T**2 * +( A(34)+A(35)*z+A(36)*z**2+A(37)*z**3+A(38)*z**4 * +A(39)*z**5+A(40)*z**6+A(41)*z**7 +A(42)*z**8 * +A(43)*z**9 +A(44)*z**10 )*T**3 * +( A(45)+A(46)*z+A(47)*z**2+A(48)*z**3+A(49)*z**4 * +A(50)*z**5+A(51)*z**6+A(52)*z**7 +A(53)*z**8 * +A(54)*z**9 +A(55)*z**10 )*T**4 * +( A(56)+A(57)*z+A(58)*z**2+A(59)*z**3+A(60)*z**4 * +A(61)*z**5+A(62)*z**6+A(63)*z**7 +A(64)*z**8 * +A(65)*z**9 +A(66)*z**10 )*T**5 * +( A(67)+A(68)*z+A(69)*z**2+A(70)*z**3+A(71)*z**4 * +A(72)*z**5+A(73)*z**6+A(74)*z**7 +A(75)*z**8 * +A(76)*z**9 +A(77)*z**10 )*T**6 * +( A(78)+A(79)*z+A(80)*z**2+A(81)*z**3+A(82)*z**4 * +A(83)*z**5+A(84)*z**6+A(85)*z**7 +A(86)*z**8 * +A(87)*z**9 +A(88)*z**10 )*T**7 * +( A(89)+A(90)*z+A(91)*z**2+A(92)*z**3+A(93)*z**4 * +A(94)*z**5+A(95)*z**6+A(96)*z**7 +A(97)*z**8 * +A(98)*z**9 +A(99)*z**10 )*T**8 * +( A(100)+A(101)*z+A(102)*z**2+A(103)*z**3+A(104)*z**4 * +A(105)*z**5+A(106)*z**6+A(107)*z**7+A(108)*z**8 * +A(109)*z**9+A(110)*z**10)*T**9 * +( A(111)+A(112)*z+A(113)*z**2+A(114)*z**3+A(115)*z**4 * +A(116)*z**5+A(117)*z**6+A(118)*z**7+A(119)*z**8 * +A(120)*z**9+A(121)*z**10)*T**10 write(6,*) zi,ti,ingco 2 continue 1 continue STOP END cccccccccccccccccccccccccccccccccccccccccccccccccccccccc c the fitting fomula of N.R. integrated Gaunt factor c cccccccccccccccccccccccccccccccccccccccccccccccccccccccc c ccccccccccccccccccccccccccccccccc c gi = log10(gamma^2) c c log10(gamma^2)= -3-->2 c c ccccccccccccccccccccccccccccccccc implicit real*8(a-z) real*8 b(11) data b/1.42752D+00,1.70677D-01,-8.13616D-01,-4.88059D-01, *1.33141D+00,7.27788D-01,-1.50917D+00,-5.99317D-01,9.86146D-01, *1.99586D-01,-2.72392D-01/ ccccccccccccccccccccccccccccccccccccccccccccc c Here users determine. c ccccccccccccccccccccccccccccccccccccccccccccc gi1 = -3.d0 gi2 = 2.d0 gd = 0.1d0 ccccccccc do 1 gi = gi1,gi2,gd ga = ( gi + 0.5d0 )/2.5d0 ingnr = b(1) * +b(2)*GA+b(3)*GA**2+b(4)*GA**3+b(5)*GA**4+b(6)*GA**5 * +b(7)*GA**6+b(8)*GA**7+b(9)*GA**8+b(10)*GA**9+b(11)*GA**10 write(6,*)gi,ingnr 1 continue stop END