From 3401c5d65f86ebc7df1b145190368cc76e72ddae Mon Sep 17 00:00:00 2001 From: Adam Nelson Date: Sat, 3 Oct 2015 10:34:56 -0400 Subject: [PATCH] Updated calc_rn to use same normalization scheme as scipys associatd legendres --- src/math.F90 | 238 +++++++++++++++++++++++++-------------------------- 1 file changed, 119 insertions(+), 119 deletions(-) diff --git a/src/math.F90 b/src/math.F90 index cd6f5567f4..51fcf36393 100644 --- a/src/math.F90 +++ b/src/math.F90 @@ -191,364 +191,364 @@ contains rn(1) = ONE case (1) ! l = 1, m = -1 - rn(1) = ONE*sqrt(w2m1) * sin(phi) + rn(1) = -(ONE*sqrt(w2m1) * sin(phi)) ! l = 1, m = 0 rn(2) = ONE * w ! l = 1, m = 1 - rn(3) = ONE*sqrt(w2m1) * cos(phi) + rn(3) = -(ONE*sqrt(w2m1) * cos(phi)) case (2) ! l = 2, m = -2 rn(1) = 0.288675134594813_8 * (-THREE * w**2 + THREE) * sin(TWO*phi) ! l = 2, m = -1 - rn(2) = 1.73205080756888_8 * w*sqrt(w2m1) * sin(phi) + rn(2) = -(1.73205080756888_8 * w*sqrt(w2m1) * sin(phi)) ! l = 2, m = 0 rn(3) = 1.5_8 * w**2 - HALF ! l = 2, m = 1 - rn(4) = 1.73205080756888_8 * w*sqrt(w2m1) * cos(phi) + rn(4) = -(1.73205080756888_8 * w*sqrt(w2m1) * cos(phi)) ! l = 2, m = 2 rn(5) = 0.288675134594813_8 * (-THREE * w**2 + THREE) * cos(TWO*phi) case (3) ! l = 3, m = -3 - rn(1) = 0.790569415042095_8 * (w2m1)**(THREE/TWO) * sin(THREE * phi) + rn(1) = -(0.790569415042095_8 * (w2m1)**(THREE/TWO) * sin(THREE * phi)) ! l = 3, m = -2 rn(2) = 1.93649167310371_8 * w*(w2m1) * sin(TWO*phi) ! l = 3, m = -1 - rn(3) = 0.408248290463863_8*sqrt(w2m1)*((15.0_8/TWO)*w**2 - THREE/TWO) * & - sin(phi) + rn(3) = -(0.408248290463863_8*sqrt(w2m1)*((15.0_8/TWO)*w**2 - THREE/TWO) * & + sin(phi)) ! l = 3, m = 0 rn(4) = 2.5_8 * w**3 - 1.5_8 * w ! l = 3, m = 1 - rn(5) = 0.408248290463863_8*sqrt(w2m1)*((15.0_8/TWO)*w**2 - THREE/TWO) * & - cos(phi) + rn(5) = -(0.408248290463863_8*sqrt(w2m1)*((15.0_8/TWO)*w**2 - THREE/TWO) * & + cos(phi)) ! l = 3, m = 2 rn(6) = 1.93649167310371_8 * w*(w2m1) * cos(TWO*phi) ! l = 3, m = 3 - rn(7) = 0.790569415042095_8 * (w2m1)**(THREE/TWO) * cos(THREE* phi) + rn(7) = -(0.790569415042095_8 * (w2m1)**(THREE/TWO) * cos(THREE* phi)) case (4) ! l = 4, m = -4 rn(1) = 0.739509972887452_8 * (w2m1)**2 * sin(4.0_8*phi) ! l = 4, m = -3 - rn(2) = 2.09165006633519_8 * w*(w2m1)**(THREE/TWO) * sin(THREE* phi) + rn(2) = -(2.09165006633519_8 * w*(w2m1)**(THREE/TWO) * sin(THREE* phi)) ! l = 4, m = -2 rn(3) = 0.074535599249993_8 * (w2m1)*((105.0_8/TWO)*w**2 - 15.0_8/TWO) * & sin(TWO*phi) ! l = 4, m = -1 - rn(4) = 0.316227766016838_8*sqrt(w2m1)*((35.0_8/TWO)*w**3 - 15.0_8/TWO*w)& - * sin(phi) + rn(4) = -(0.316227766016838_8*sqrt(w2m1)*((35.0_8/TWO)*w**3 - 15.0_8/TWO*w)& + * sin(phi)) ! l = 4, m = 0 rn(5) = 4.375_8 * w**4 - 3.75_8 * w**2 + 0.375_8 ! l = 4, m = 1 - rn(6) = 0.316227766016838_8*sqrt(w2m1)*((35.0_8/TWO)*w**3 - 15.0_8/TWO*w)& - * cos(phi) + rn(6) = -(0.316227766016838_8*sqrt(w2m1)*((35.0_8/TWO)*w**3 - 15.0_8/TWO*w)& + * cos(phi)) ! l = 4, m = 2 rn(7) = 0.074535599249993_8 * (w2m1)*((105.0_8/TWO)*w**2 - 15.0_8/TWO) * & cos(TWO*phi) ! l = 4, m = 3 - rn(8) = 2.09165006633519_8 * w*(w2m1)**(THREE/TWO) * cos(THREE* phi) + rn(8) = -(2.09165006633519_8 * w*(w2m1)**(THREE/TWO) * cos(THREE* phi)) ! l = 4, m = 4 rn(9) = 0.739509972887452_8 * (w2m1)**2 * cos(4.0_8*phi) case (5) ! l = 5, m = -5 - rn(1) = 0.701560760020114_8 * (w2m1)**(5.0_8/TWO) * sin(5.0_8*phi) + rn(1) = -(0.701560760020114_8 * (w2m1)**(5.0_8/TWO) * sin(5.0_8*phi)) ! l = 5, m = -4 rn(2) = 2.21852991866236_8 * w*(w2m1)**2 * sin(4.0_8*phi) ! l = 5, m = -3 - rn(3) = 0.00996023841111995_8 * (w2m1)**(THREE/TWO)* & - ((945.0_8 /TWO)*w**2 - 105.0_8/TWO) * sin(THREE*phi) + rn(3) = -(0.00996023841111995_8 * (w2m1)**(THREE/TWO)* & + ((945.0_8 /TWO)*w**2 - 105.0_8/TWO) * sin(THREE*phi)) ! l = 5, m = -2 rn(4) = 0.0487950036474267_8 * (w2m1) & * ((315.0_8/TWO)*w**3 - 105.0_8/TWO*w) * sin(TWO*phi) ! l = 5, m = -1 - rn(5) = 0.258198889747161_8*sqrt(w2m1)* & + rn(5) = -(0.258198889747161_8*sqrt(w2m1)* & ((315.0_8/8.0_8)*w**4 - 105.0_8/4.0_8 * w**2 + 15.0_8/8.0_8) & - * sin(phi) + * sin(phi)) ! l = 5, m = 0 rn(6) = 7.875_8 * w**5 - 8.75_8 * w**3 + 1.875_8 * w ! l = 5, m = 1 - rn(7) = 0.258198889747161_8*sqrt(w2m1)* & + rn(7) = -(0.258198889747161_8*sqrt(w2m1)* & ((315.0_8/8.0_8)*w**4 - 105.0_8/4.0_8 * w**2 + 15.0_8/8.0_8) & - * cos(phi) + * cos(phi)) ! l = 5, m = 2 rn(8) = 0.0487950036474267_8 * (w2m1)* & ((315.0_8/TWO)*w**3 - 105.0_8/TWO*w) * cos(TWO*phi) ! l = 5, m = 3 - rn(9) = 0.00996023841111995_8 * (w2m1)**(THREE/TWO)* & - ((945.0_8 /TWO)*w**2 - 105.0_8/TWO) * cos(THREE*phi) + rn(9) = -(0.00996023841111995_8 * (w2m1)**(THREE/TWO)* & + ((945.0_8 /TWO)*w**2 - 105.0_8/TWO) * cos(THREE*phi)) ! l = 5, m = 4 rn(10) = 2.21852991866236_8 * w*(w2m1)**2 * cos(4.0_8*phi) ! l = 5, m = 5 - rn(11) = 0.701560760020114_8 * (w2m1)**(5.0_8/TWO) * cos(5.0_8* phi) + rn(11) = -(0.701560760020114_8 * (w2m1)**(5.0_8/TWO) * cos(5.0_8* phi)) case (6) ! l = 6, m = -6 rn(1) = 0.671693289381396_8 * (w2m1)**3 * sin(6.0_8*phi) ! l = 6, m = -5 - rn(2) = 2.32681380862329_8 * w*(w2m1)**(5.0_8/TWO) * sin(5.0_8*phi) + rn(2) = -(2.32681380862329_8 * w*(w2m1)**(5.0_8/TWO) * sin(5.0_8*phi)) ! l = 6, m = -4 rn(3) = 0.00104990131391452_8 * (w2m1)**2 * & ((10395.0_8/TWO)*w**2 - 945.0_8/TWO) * sin(4.0_8*phi) ! l = 6, m = -3 - rn(4) = 0.00575054632785295_8 * (w2m1)**(THREE/TWO) * & - ((3465.0_8/TWO)*w**3 - 945.0_8/TWO*w) * sin(THREE*phi) + rn(4) = -(0.00575054632785295_8 * (w2m1)**(THREE/TWO) * & + ((3465.0_8/TWO)*w**3 - 945.0_8/TWO*w) * sin(THREE*phi)) ! l = 6, m = -2 rn(5) = 0.0345032779671177_8 * (w2m1) * & ((3465.0_8/8.0_8)*w**4 - 945.0_8/4.0_8 * w**2 + 105.0_8/8.0_8) & * sin(TWO*phi) ! l = 6, m = -1 - rn(6) = 0.218217890235992_8*sqrt(w2m1) * & + rn(6) = -(0.218217890235992_8*sqrt(w2m1) * & ((693.0_8/8.0_8)*w**5- 315.0_8/4.0_8 * w**3 + (105.0_8/8.0_8)*w) & - * sin(phi) + * sin(phi)) ! l = 6, m = 0 rn(7) = 14.4375_8 * w**6 - 19.6875_8 * w**4 + 6.5625_8 * w**2 - 0.3125_8 ! l = 6, m = 1 - rn(8) = 0.218217890235992_8*sqrt(w2m1) * & + rn(8) = -(0.218217890235992_8*sqrt(w2m1) * & ((693.0_8/8.0_8)*w**5- 315.0_8/4.0_8 * w**3 + (105.0_8/8.0_8)*w) & - * cos(phi) + * cos(phi)) ! l = 6, m = 2 rn(9) = 0.0345032779671177_8 * (w2m1) * & ((3465.0_8/8.0_8)*w**4 -945.0_8/4.0_8 * w**2 + 105.0_8/8.0_8) & * cos(TWO*phi) ! l = 6, m = 3 - rn(10) = 0.00575054632785295_8 * (w2m1)**(THREE/TWO) * & - ((3465.0_8/TWO)*w**3 - 945.0_8/TWO*w) * cos(THREE*phi) + rn(10) = -(0.00575054632785295_8 * (w2m1)**(THREE/TWO) * & + ((3465.0_8/TWO)*w**3 - 945.0_8/TWO*w) * cos(THREE*phi)) ! l = 6, m = 4 rn(11) = 0.00104990131391452_8 * (w2m1)**2 * & ((10395.0_8/TWO)*w**2 - 945.0_8/TWO) * cos(4.0_8*phi) ! l = 6, m = 5 - rn(12) = 2.32681380862329_8 * w*(w2m1)**(5.0_8/TWO) * cos(5.0_8*phi) + rn(12) = -(2.32681380862329_8 * w*(w2m1)**(5.0_8/TWO) * cos(5.0_8*phi)) ! l = 6, m = 6 rn(13) = 0.671693289381396_8 * (w2m1)**3 * cos(6.0_8*phi) case (7) ! l = 7, m = -7 - rn(1) = 0.647259849287749_8 * (w2m1)**(7.0_8/TWO) * sin(7.0_8*phi) + rn(1) = -(0.647259849287749_8 * (w2m1)**(7.0_8/TWO) * sin(7.0_8*phi)) ! l = 7, m = -6 rn(2) = 2.42182459624969_8 * w*(w2m1)**3 * sin(6.0_8*phi) ! l = 7, m = -5 - rn(3) = 9.13821798555235d-5*(w2m1)**(5.0_8/TWO)* & - ((135135.0_8/TWO)*w**2 - 10395.0_8/TWO) * sin(5.0_8*phi) + rn(3) = -(9.13821798555235d-5*(w2m1)**(5.0_8/TWO)* & + ((135135.0_8/TWO)*w**2 - 10395.0_8/TWO) * sin(5.0_8*phi)) ! l = 7, m = -4 rn(4) = 0.000548293079133141_8 * (w2m1)**2* & ((45045.0_8/TWO)*w**3 - 10395.0_8/TWO*w) * sin(4.0_8*phi) ! l = 7, m = -3 - rn(5) = 0.00363696483726654_8 * (w2m1)**(THREE/TWO)* & - ((45045.0_8/8.0_8)*w**4 - 10395.0_8/4.0_8 * w**2 + 945.0_8/8.0_8)* & - sin(THREE*phi) + rn(5) = -(0.00363696483726654_8 * (w2m1)**(THREE/TWO)* & + ((45045.0_8/8.0_8)*w**4 - 10395.0_8/4.0_8 * w**2 + 945.0_8/8.0_8)* & + sin(THREE*phi)) ! l = 7, m = -2 rn(6) = 0.025717224993682_8 * (w2m1)* & ((9009.0_8/8.0_8)*w**5 -3465.0_8/4.0_8 * w**3 + (945.0_8/8.0_8)*w)* & sin(TWO*phi) ! l = 7, m = -1 - rn(7) = 0.188982236504614_8*sqrt(w2m1)* & - ((3003.0_8/16.0_8)*w**6 - 3465.0_8/16.0_8 * w**4 + & - (945.0_8/16.0_8)*w**2 - 35.0_8/16.0_8) * sin(phi) + rn(7) = -(0.188982236504614_8*sqrt(w2m1)* & + ((3003.0_8/16.0_8)*w**6 - 3465.0_8/16.0_8 * w**4 + & + (945.0_8/16.0_8)*w**2 - 35.0_8/16.0_8) * sin(phi)) ! l = 7, m = 0 rn(8) = 26.8125_8 * w**7 - 43.3125_8 * w**5 + 19.6875_8 * w**3 -2.1875_8 & * w ! l = 7, m = 1 - rn(9) = 0.188982236504614_8*sqrt(w2m1)* & - ((3003.0_8/16.0_8)*w**6 - 3465.0_8/16.0_8 * w**4 + & - (945.0_8/16.0_8)*w**2 - 35.0_8/16.0_8) * cos(phi) + rn(9) = -(0.188982236504614_8*sqrt(w2m1)* & + ((3003.0_8/16.0_8)*w**6 - 3465.0_8/16.0_8 * w**4 + & + (945.0_8/16.0_8)*w**2 - 35.0_8/16.0_8) * cos(phi)) ! l = 7, m = 2 rn(10) = 0.025717224993682_8 * (w2m1)* & ((9009.0_8/8.0_8)*w**5 -3465.0_8/4.0_8 * w**3 + (945.0_8/8.0_8)*w)* & cos(TWO*phi) ! l = 7, m = 3 - rn(11) = 0.00363696483726654_8 * (w2m1)**(THREE/TWO)* & - ((45045.0_8/8.0_8)*w**4 - 10395.0_8/4.0_8 * w**2 + 945.0_8/8.0_8)* & - cos(THREE*phi) + rn(11) = -(0.00363696483726654_8 * (w2m1)**(THREE/TWO)* & + ((45045.0_8/8.0_8)*w**4 - 10395.0_8/4.0_8 * w**2 + 945.0_8/8.0_8)* & + cos(THREE*phi)) ! l = 7, m = 4 rn(12) = 0.000548293079133141_8 * (w2m1)**2 * & ((45045.0_8/TWO)*w**3 - 10395.0_8/TWO*w) * cos(4.0_8*phi) ! l = 7, m = 5 - rn(13) = 9.13821798555235d-5*(w2m1)**(5.0_8/TWO)* & - ((135135.0_8/TWO)*w**2 - 10395.0_8/TWO) * cos(5.0_8*phi) + rn(13) = -(9.13821798555235d-5*(w2m1)**(5.0_8/TWO)* & + ((135135.0_8/TWO)*w**2 - 10395.0_8/TWO) * cos(5.0_8*phi)) ! l = 7, m = 6 rn(14) = 2.42182459624969_8 * w*(w2m1)**3 * cos(6.0_8*phi) ! l = 7, m = 7 - rn(15) = 0.647259849287749_8 * (w2m1)**(7.0_8/TWO) * cos(7.0_8*phi) + rn(15) = -(0.647259849287749_8 * (w2m1)**(7.0_8/TWO) * cos(7.0_8*phi)) case (8) ! l = 8, m = -8 rn(1) = 0.626706654240044_8 * (w2m1)**4 * sin(8.0_8*phi) ! l = 8, m = -7 - rn(2) = 2.50682661696018_8 * w*(w2m1)**(7.0_8/TWO) * sin(7.0_8*phi) + rn(2) = -(2.50682661696018_8 * w*(w2m1)**(7.0_8/TWO) * sin(7.0_8*phi)) ! l = 8, m = -6 rn(3) = 6.77369783729086d-6*(w2m1)**3* & ((2027025.0_8/TWO)*w**2 - 135135.0_8/TWO) * sin(6.0_8*phi) ! l = 8, m = -5 - rn(4) = 4.38985792528482d-5*(w2m1)**(5.0_8/TWO)* & - ((675675.0_8/TWO)*w**3 - 135135.0_8/TWO*w) * sin(5.0_8*phi) + rn(4) = -(4.38985792528482d-5*(w2m1)**(5.0_8/TWO)* & + ((675675.0_8/TWO)*w**3 - 135135.0_8/TWO*w) * sin(5.0_8*phi)) ! l = 8, m = -4 rn(5) = 0.000316557156832328_8 * (w2m1)**2* & ((675675.0_8/8.0_8)*w**4 - 135135.0_8/4.0_8 * w**2 & + 10395.0_8/8.0_8) * sin(4.0_8*phi) ! l = 8, m = -3 - rn(6) = 0.00245204119306875_8 * (w2m1)**(THREE/TWO)* & - ((135135.0_8/8.0_8)*w**5 - 45045.0_8/4.0_8 * w**3 & - + (10395.0_8/8.0_8)*w) * sin(THREE*phi) + rn(6) = -(0.00245204119306875_8 * (w2m1)**(THREE/TWO)* & + ((135135.0_8/8.0_8)*w**5 - 45045.0_8/4.0_8 * w**3 & + + (10395.0_8/8.0_8)*w) * sin(THREE*phi)) ! l = 8, m = -2 rn(7) = 0.0199204768222399_8 * (w2m1)* & ((45045.0_8/16.0_8)*w**6- 45045.0_8/16.0_8 * w**4 + & (10395.0_8/16.0_8)*w**2 - 315.0_8/16.0_8) * sin(TWO*phi) ! l = 8, m = -1 - rn(8) = 0.166666666666667_8*sqrt(w2m1)* & - ((6435.0_8/16.0_8)*w**7 - 9009.0_8/16.0_8 * w**5 + & - (3465.0_8/16.0_8)*w**3 - 315.0_8/16.0_8 * w) * sin(phi) + rn(8) = -(0.166666666666667_8*sqrt(w2m1)* & + ((6435.0_8/16.0_8)*w**7 - 9009.0_8/16.0_8 * w**5 + & + (3465.0_8/16.0_8)*w**3 - 315.0_8/16.0_8 * w) * sin(phi)) ! l = 8, m = 0 rn(9) = 50.2734375_8 * w**8 - 93.84375_8 * w**6 + 54.140625_8 * w**4 -& 9.84375_8 * w**2 + 0.2734375_8 ! l = 8, m = 1 - rn(10) = 0.166666666666667_8*sqrt(w2m1)* & - ((6435.0_8/16.0_8)*w**7 - 9009.0_8/16.0_8 * w**5 + & - (3465.0_8/16.0_8)*w**3 - 315.0_8/16.0_8 * w) * cos(phi) + rn(10) = -(0.166666666666667_8*sqrt(w2m1)* & + ((6435.0_8/16.0_8)*w**7 - 9009.0_8/16.0_8 * w**5 + & + (3465.0_8/16.0_8)*w**3 - 315.0_8/16.0_8 * w) * cos(phi)) ! l = 8, m = 2 rn(11) = 0.0199204768222399_8 * (w2m1)*((45045.0_8/16.0_8)*w**6- & 45045.0_8/16.0_8 * w**4 + (10395.0_8/16.0_8)*w**2 - & 315.0_8/16.0_8) * cos(TWO*phi) ! l = 8, m = 3 - rn(12) = 0.00245204119306875_8 * (w2m1)**(THREE/TWO)* & - ((135135.0_8/8.0_8)*w**5 - 45045.0_8/4.0_8 * w**3 + & - (10395.0_8/8.0_8)*w) * cos(THREE*phi) + rn(12) = -(0.00245204119306875_8 * (w2m1)**(THREE/TWO)* & + ((135135.0_8/8.0_8)*w**5 - 45045.0_8/4.0_8 * w**3 + & + (10395.0_8/8.0_8)*w) * cos(THREE*phi)) ! l = 8, m = 4 rn(13) = 0.000316557156832328_8 * (w2m1)**2*((675675.0_8/8.0_8)*w**4 - & 135135.0_8/4.0_8 * w**2 + 10395.0_8/8.0_8) * cos(4.0_8*phi) ! l = 8, m = 5 - rn(14) = 4.38985792528482d-5*(w2m1)**(5.0_8/TWO)*((675675.0_8/TWO)*w**3 -& - 135135.0_8/TWO*w) * cos(5.0_8*phi) + rn(14) = -(4.38985792528482d-5*(w2m1)**(5.0_8/TWO)*((675675.0_8/TWO)*w**3 -& + 135135.0_8/TWO*w) * cos(5.0_8*phi)) ! l = 8, m = 6 rn(15) = 6.77369783729086d-6*(w2m1)**3*((2027025.0_8/TWO)*w**2 - & 135135.0_8/TWO) * cos(6.0_8*phi) ! l = 8, m = 7 - rn(16) = 2.50682661696018_8 * w*(w2m1)**(7.0_8/TWO) * cos(7.0_8*phi) + rn(16) = -(2.50682661696018_8 * w*(w2m1)**(7.0_8/TWO) * cos(7.0_8*phi)) ! l = 8, m = 8 rn(17) = 0.626706654240044_8 * (w2m1)**4 * cos(8.0_8*phi) case (9) ! l = 9, m = -9 - rn(1) = 0.609049392175524_8 * (w2m1)**(9.0_8/TWO) * sin(9.0_8*phi) + rn(1) = -(0.609049392175524_8 * (w2m1)**(9.0_8/TWO) * sin(9.0_8*phi)) ! l = 9, m = -8 rn(2) = 2.58397773170915_8 * w*(w2m1)**4 * sin(8.0_8*phi) ! l = 9, m = -7 - rn(3) = 4.37240315267812d-7*(w2m1)**(7.0_8/TWO)* & - ((34459425.0_8/TWO)*w**2 - 2027025.0_8/TWO) * sin(7.0_8*phi) + rn(3) = -(4.37240315267812d-7*(w2m1)**(7.0_8/TWO)* & + ((34459425.0_8/TWO)*w**2 - 2027025.0_8/TWO) * sin(7.0_8*phi)) ! l = 9, m = -6 rn(4) = 3.02928976464514d-6*(w2m1)**3* & ((11486475.0_8/TWO)*w**3 - 2027025.0_8/TWO*w) * sin(6.0_8*phi) ! l = 9, m = -5 - rn(5) = 2.34647776186144d-5*(w2m1)**(5.0_8/TWO)* & - ((11486475.0_8/8.0_8)*w**4 - 2027025.0_8/4.0_8 * w**2 + & - 135135.0_8/8.0_8) * sin(5.0_8*phi) + rn(5) = -(2.34647776186144d-5*(w2m1)**(5.0_8/TWO)* & + ((11486475.0_8/8.0_8)*w**4 - 2027025.0_8/4.0_8 * w**2 + & + 135135.0_8/8.0_8) * sin(5.0_8*phi)) ! l = 9, m = -4 rn(6) = 0.000196320414650061_8 * (w2m1)**2*((2297295.0_8/8.0_8)*w**5 - & 675675.0_8/4.0_8 * w**3 + (135135.0_8/8.0_8)*w) * sin(4.0_8*phi) ! l = 9, m = -3 - rn(7) = 0.00173385495536766_8 * (w2m1)**(THREE/TWO)* & - ((765765.0_8/16.0_8)*w**6 - 675675.0_8/16.0_8 * w**4 + & - (135135.0_8/16.0_8)*w**2 - 3465.0_8/16.0_8) * sin(THREE*phi) + rn(7) = -(0.00173385495536766_8 * (w2m1)**(THREE/TWO)* & + ((765765.0_8/16.0_8)*w**6 - 675675.0_8/16.0_8 * w**4 + & + (135135.0_8/16.0_8)*w**2 - 3465.0_8/16.0_8) * sin(THREE*phi)) ! l = 9, m = -2 rn(8) = 0.0158910431540932_8 * (w2m1)*((109395.0_8/16.0_8)*w**7- & 135135.0_8/16.0_8 * w**5 + (45045.0_8/16.0_8)*w**3 & - 3465.0_8/16.0_8 * w) * sin(TWO*phi) ! l = 9, m = -1 - rn(9) = 0.149071198499986_8*sqrt(w2m1)*((109395.0_8/128.0_8)*w**8 - & - 45045.0_8/32.0_8 * w**6 + (45045.0_8/64.0_8)*w**4 - 3465.0_8/32.0_8 & - * w**2 + 315.0_8/128.0_8) * sin(phi) + rn(9) = -(0.149071198499986_8*sqrt(w2m1)*((109395.0_8/128.0_8)*w**8 - & + 45045.0_8/32.0_8 * w**6 + (45045.0_8/64.0_8)*w**4 - 3465.0_8/32.0_8 & + * w**2 + 315.0_8/128.0_8) * sin(phi)) ! l = 9, m = 0 rn(10) = 94.9609375_8 * w**9 - 201.09375_8 * w**7 + 140.765625_8 * w**5- & 36.09375_8 * w**3 + 2.4609375_8 * w ! l = 9, m = 1 - rn(11) = 0.149071198499986_8*sqrt(w2m1)*((109395.0_8/128.0_8)*w**8 - & - 45045.0_8/32.0_8 * w**6 + (45045.0_8/64.0_8)*w**4 -3465.0_8/32.0_8 & - * w**2 + 315.0_8/128.0_8) * cos(phi) + rn(11) = -(0.149071198499986_8*sqrt(w2m1)*((109395.0_8/128.0_8)*w**8 - & + 45045.0_8/32.0_8 * w**6 + (45045.0_8/64.0_8)*w**4 -3465.0_8/32.0_8 & + * w**2 + 315.0_8/128.0_8) * cos(phi)) ! l = 9, m = 2 rn(12) = 0.0158910431540932_8 * (w2m1)*((109395.0_8/16.0_8)*w**7 - & 135135.0_8/16.0_8 * w**5 + (45045.0_8/16.0_8)*w**3 & - 3465.0_8/ 16.0_8 * w) * cos(TWO*phi) ! l = 9, m = 3 - rn(13) = 0.00173385495536766_8 * (w2m1)**(THREE/TWO)*((765765.0_8/16.0_8)& - *w**6 - 675675.0_8/16.0_8 * w**4 + (135135.0_8/16.0_8)*w**2 & - - 3465.0_8/16.0_8)* cos(THREE*phi) + rn(13) = -(0.00173385495536766_8 * (w2m1)**(THREE/TWO)*((765765.0_8/16.0_8)& + *w**6 - 675675.0_8/16.0_8 * w**4 + (135135.0_8/16.0_8)*w**2 & + - 3465.0_8/16.0_8)* cos(THREE*phi)) ! l = 9, m = 4 rn(14) = 0.000196320414650061_8 * (w2m1)**2*((2297295.0_8/8.0_8)*w**5 - & 675675.0_8/4.0_8 * w**3 + (135135.0_8/8.0_8)*w) * cos(4.0_8*phi) ! l = 9, m = 5 - rn(15) = 2.34647776186144d-5*(w2m1)**(5.0_8/TWO)*((11486475.0_8/8.0_8)* & - w**4 - 2027025.0_8/4.0_8 * w**2 + 135135.0_8/8.0_8) * cos(5.0_8*phi) + rn(15) = -(2.34647776186144d-5*(w2m1)**(5.0_8/TWO)*((11486475.0_8/8.0_8)* & + w**4 - 2027025.0_8/4.0_8 * w**2 + 135135.0_8/8.0_8) * cos(5.0_8*phi)) ! l = 9, m = 6 rn(16) = 3.02928976464514d-6*(w2m1)**3*((11486475.0_8/TWO)*w**3 - & 2027025.0_8/TWO*w) * cos(6.0_8*phi) ! l = 9, m = 7 - rn(17) = 4.37240315267812d-7*(w2m1)**(7.0_8/TWO)* & - ((34459425.0_8/TWO)*w**2 - 2027025.0_8/TWO) * cos(7.0_8*phi) + rn(17) = -(4.37240315267812d-7*(w2m1)**(7.0_8/TWO)* & + ((34459425.0_8/TWO)*w**2 - 2027025.0_8/TWO) * cos(7.0_8*phi)) ! l = 9, m = 8 rn(18) = 2.58397773170915_8 * w*(w2m1)**4 * cos(8.0_8*phi) ! l = 9, m = 9 - rn(19) = 0.609049392175524_8 * (w2m1)**(9.0_8/TWO) * cos(9.0_8*phi) + rn(19) = -(0.609049392175524_8 * (w2m1)**(9.0_8/TWO) * cos(9.0_8*phi)) case (10) ! l = 10, m = -10 rn(1) = 0.593627917136573_8 * (w2m1)**5 * sin(10.0_8*phi) ! l = 10, m = -9 - rn(2) = 2.65478475211798_8 * w*(w2m1)**(9.0_8/TWO) * sin(9.0_8*phi) + rn(2) = -(2.65478475211798_8 * w*(w2m1)**(9.0_8/TWO) * sin(9.0_8*phi)) ! l = 10, m = -8 rn(3) = 2.49953651452314d-8*(w2m1)**4*((654729075.0_8/TWO)*w**2 - & 34459425.0_8/TWO) * sin(8.0_8*phi) ! l = 10, m = -7 - rn(4) = 1.83677671621093d-7*(w2m1)**(7.0_8/TWO)* & - ((218243025.0_8/TWO)*w**3 - 34459425.0_8/TWO*w) * sin(7.0_8*phi) + rn(4) = -(1.83677671621093d-7*(w2m1)**(7.0_8/TWO)* & + ((218243025.0_8/TWO)*w**3 - 34459425.0_8/TWO*w) * sin(7.0_8*phi)) ! l = 10, m = -6 rn(5) = 1.51464488232257d-6*(w2m1)**3*((218243025.0_8/8.0_8)*w**4 - & 34459425.0_8/4.0_8 * w**2 + 2027025.0_8/8.0_8) * sin(6.0_8*phi) ! l = 10, m = -5 - rn(6) = 1.35473956745817d-5*(w2m1)**(5.0_8/TWO)* & - ((43648605.0_8/8.0_8)*w**5 - 11486475.0_8/4.0_8 * w**3 + & - (2027025.0_8/8.0_8)*w) * sin(5.0_8*phi) + rn(6) = -(1.35473956745817d-5*(w2m1)**(5.0_8/TWO)* & + ((43648605.0_8/8.0_8)*w**5 - 11486475.0_8/4.0_8 * w**3 + & + (2027025.0_8/8.0_8)*w) * sin(5.0_8*phi)) ! l = 10, m = -4 rn(7) = 0.000128521880085575_8 * (w2m1)**2*((14549535.0_8/16.0_8)*w**6 - & 11486475.0_8/16.0_8 * w**4 + (2027025.0_8/16.0_8)*w**2 - & 45045.0_8/16.0_8) * sin(4.0_8*phi) ! l = 10, m = -3 - rn(8) = 0.00127230170115096_8 * (w2m1)**(THREE/TWO)* & - ((2078505.0_8/16.0_8)*w**7 - 2297295.0_8/16.0_8 * w**5 + & - (675675.0_8/16.0_8)*w**3 - 45045.0_8/16.0_8 * w) * sin(THREE*phi) + rn(8) = -(0.00127230170115096_8 * (w2m1)**(THREE/TWO)* & + ((2078505.0_8/16.0_8)*w**7 - 2297295.0_8/16.0_8 * w**5 + & + (675675.0_8/16.0_8)*w**3 - 45045.0_8/16.0_8 * w) * sin(THREE*phi)) ! l = 10, m = -2 rn(9) = 0.012974982402692_8 * (w2m1)*((2078505.0_8/128.0_8)*w**8 - & 765765.0_8/32.0_8 * w**6 + (675675.0_8/64.0_8)*w**4 - & 45045.0_8/32.0_8 * w**2 + 3465.0_8/128.0_8) * sin(TWO*phi) ! l = 10, m = -1 - rn(10) = 0.134839972492648_8*sqrt(w2m1)*((230945.0_8/128.0_8)*w**9 - & - 109395.0_8/32.0_8 * w**7 + (135135.0_8/64.0_8)*w**5 - & - 15015.0_8/32.0_8 * w**3 + (3465.0_8/128.0_8)*w) * sin(phi) + rn(10) = -(0.134839972492648_8*sqrt(w2m1)*((230945.0_8/128.0_8)*w**9 - & + 109395.0_8/32.0_8 * w**7 + (135135.0_8/64.0_8)*w**5 - & + 15015.0_8/32.0_8 * w**3 + (3465.0_8/128.0_8)*w) * sin(phi)) ! l = 10, m = 0 rn(11) = 180.42578125_8 * w**10 - 427.32421875_8 * w**8 +351.9140625_8 & * w**6 - 117.3046875_8 * w**4 + 13.53515625_8 * w**2 -0.24609375_8 ! l = 10, m = 1 - rn(12) = 0.134839972492648_8*sqrt(w2m1)*((230945.0_8/128.0_8)*w**9 - & - 109395.0_8/32.0_8 * w**7 + (135135.0_8/64.0_8)*w**5 -15015.0_8/ & - 32.0_8 * w**3 + (3465.0_8/128.0_8)*w) * cos(phi) + rn(12) = -(0.134839972492648_8*sqrt(w2m1)*((230945.0_8/128.0_8)*w**9 - & + 109395.0_8/32.0_8 * w**7 + (135135.0_8/64.0_8)*w**5 -15015.0_8/ & + 32.0_8 * w**3 + (3465.0_8/128.0_8)*w) * cos(phi)) ! l = 10, m = 2 rn(13) = 0.012974982402692_8 * (w2m1)*((2078505.0_8/128.0_8)*w**8 - & 765765.0_8/32.0_8 * w**6 + (675675.0_8/64.0_8)*w**4 -& 45045.0_8/32.0_8 * w**2 + 3465.0_8/128.0_8) * cos(TWO*phi) ! l = 10, m = 3 - rn(14) = 0.00127230170115096_8 * (w2m1)**(THREE/TWO)* & - ((2078505.0_8/16.0_8)*w**7 - 2297295.0_8/16.0_8 * w**5 + & - (675675.0_8/16.0_8)*w**3 - 45045.0_8/16.0_8 * w) * cos(THREE*phi) + rn(14) = -(0.00127230170115096_8 * (w2m1)**(THREE/TWO)* & + ((2078505.0_8/16.0_8)*w**7 - 2297295.0_8/16.0_8 * w**5 + & + (675675.0_8/16.0_8)*w**3 - 45045.0_8/16.0_8 * w) * cos(THREE*phi)) ! l = 10, m = 4 rn(15) = 0.000128521880085575_8 * (w2m1)**2*((14549535.0_8/16.0_8)*w**6 -& 11486475.0_8/16.0_8 * w**4 + (2027025.0_8/16.0_8)*w**2 - & 45045.0_8/16.0_8) * cos(4.0_8*phi) ! l = 10, m = 5 - rn(16) = 1.35473956745817d-5*(w2m1)**(5.0_8/TWO)* & - ((43648605.0_8/8.0_8)*w**5 - 11486475.0_8/4.0_8 * w**3 + & - (2027025.0_8/8.0_8)*w) * cos(5.0_8*phi) + rn(16) = -(1.35473956745817d-5*(w2m1)**(5.0_8/TWO)* & + ((43648605.0_8/8.0_8)*w**5 - 11486475.0_8/4.0_8 * w**3 + & + (2027025.0_8/8.0_8)*w) * cos(5.0_8*phi)) ! l = 10, m = 6 rn(17) = 1.51464488232257d-6*(w2m1)**3*((218243025.0_8/8.0_8)*w**4 - & 34459425.0_8/4.0_8 * w**2 + 2027025.0_8/8.0_8) * cos(6.0_8*phi) ! l = 10, m = 7 - rn(18) = 1.83677671621093d-7*(w2m1)**(7.0_8/TWO)* & - ((218243025.0_8/TWO)*w**3 - 34459425.0_8/TWO*w) * cos(7.0_8*phi) + rn(18) = -(1.83677671621093d-7*(w2m1)**(7.0_8/TWO)* & + ((218243025.0_8/TWO)*w**3 - 34459425.0_8/TWO*w) * cos(7.0_8*phi)) ! l = 10, m = 8 rn(19) = 2.49953651452314d-8*(w2m1)**4* & ((654729075.0_8/TWO)*w**2 - 34459425.0_8/TWO) * cos(8.0_8*phi) ! l = 10, m = 9 - rn(20) = 2.65478475211798_8 * w*(w2m1)**(9.0_8/TWO) * cos(9.0_8*phi) + rn(20) = -(2.65478475211798_8 * w*(w2m1)**(9.0_8/TWO) * cos(9.0_8*phi)) ! l = 10, m = 10 rn(21) = 0.593627917136573_8 * (w2m1)**5 * cos(10.0_8*phi) case default