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read hol0;
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#Bounded polynomials of the form fni*cos(n*theta)
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F11:=-diff(F2,r);
F12:=-diff(F3,r);
F13:=-diff(F4,r);
F14:=-diff(F5,r);
F15:=-diff(F6,r):
F16:=-diff(F7,r):
F17:=-diff(F8,r):
F18:=-diff(F9,r):
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F22:=-expand(simplify(diff(F13,r)-F13/r));
F23:=-expand(simplify(diff(F14,r)-F14/r));
F24:=-expand(simplify(diff(F15,r)-F15/r));
F25:=-expand(simplify(diff(F16,r)-F16/r)):
F26:=-expand(simplify(diff(F17,r)-F17/r)):
F27:=-expand(simplify(diff(F18,r)-F18/r)):
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F33:=-expand(diff(F24,r)-2*F24/r);
F34:=-expand(diff(F25,r)-2*F25/r);
F35:=-expand(diff(F26,r)-2*F26/r):
F36:=-expand(diff(F27,r)-2*F27/r):
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#Singular potentials of the form sni*cos(n*theta)
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S10:=expand(simplify(diff(S0,r)));
S11:=expand(simplify(diff(S1,r)));
S12:=expand(simplify(diff(S2,r)));
S13:=expand(simplify(diff(S3,r)));
S14:=expand(simplify(diff(S4,r)));
S15:=expand(simplify(diff(S5,r))):
S16:=expand(simplify(diff(S6,r))):
S17:=expand(simplify(diff(S7,r))):
S18:=expand(simplify(diff(S8,r))):
S19:=expand(simplify(diff(S9,r))):
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S20:=expand(simplify(diff(S10,r)-S10/r));
S21:=expand(simplify(diff(S11,r)-S11/r));
S22:=expand(simplify(diff(S12,r)-S12/r));
S23:=expand(simplify(diff(S13,r)-S13/r));
S24:=expand(simplify(diff(S14,r)-S14/r));
S25:=expand(simplify(diff(S15,r)-S15/r)):
S26:=expand(simplify(diff(S16,r)-S16/r)):
S27:=expand(simplify(diff(S17,r)-S17/r)):
S28:=expand(simplify(diff(S18,r)-S18/r)):
S29:=expand(simplify(diff(S19,r)-S19/r)):
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S30:=expand(simplify(diff(S20,r)-2*S20/r)):
S31:=expand(simplify(diff(S21,r)-2*S21/r)):
S32:=expand(simplify(diff(S22,r)-2*S22/r)):
S33:=expand(simplify(diff(S23,r)-2*S23/r)):
S34:=expand(simplify(diff(S24,r)-2*S24/r)):
S35:=expand(simplify(diff(S25,r)-2*S25/r)):
S36:=expand(diff(S26,r)-2*S26/r):
S37:=expand(diff(S27,r)-2*S27/r):
S38:=expand(diff(S28,r)-2*S28/r):
S39:=expand(diff(S29,r)-2*S29/r):
#