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Isuue #490 improved ZTransform, HurwitzLerchPhi, PolyLog
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...core/src/main/java/org/matheclipse/core/reflection/system/rules/HurwitzLerchPhiRules.java
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| package org.matheclipse.core.reflection.system.rules; | ||
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| import static org.matheclipse.core.expression.F.*; | ||
| import org.matheclipse.core.interfaces.ISymbol; | ||
| import org.matheclipse.core.interfaces.IAST; | ||
| import org.matheclipse.core.patternmatching.Matcher; | ||
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| /** | ||
| * <p>Generated by <code>org.matheclipse.core.preprocessor.RulePreprocessor</code>.</p> | ||
| * <p>See GIT repository at: <a href="https://github.com/axkr/symja_android_library">github.com/axkr/symja_android_library under the tools directory</a>.</p> | ||
| */ | ||
| public interface HurwitzLerchPhiRules { | ||
| /** | ||
| * <ul> | ||
| * <li>index 0 - number of equal rules in <code>RULES</code></li> | ||
| * </ul> | ||
| */ | ||
| final public static int[] SIZES = { 1, 3 }; | ||
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| final public static IAST RULES = List( | ||
| IInit(HurwitzLerchPhi, SIZES), | ||
| // HurwitzLerchPhi(0,1,1)=1 | ||
| ISet(HurwitzLerchPhi(C0,C1,C1), | ||
| C1), | ||
| // HurwitzLerchPhi(z_,s_,1):=PolyLog(s,z)/z | ||
| ISetDelayed(HurwitzLerchPhi(z_,s_,C1), | ||
| Times(Power(z,CN1),PolyLog(s,z))), | ||
| // HurwitzLerchPhi(z_,0,a_):=1/(1-z) | ||
| ISetDelayed(HurwitzLerchPhi(z_,C0,a_), | ||
| Power(Subtract(C1,z),CN1)), | ||
| // HurwitzLerchPhi(0,s_,a_):=a^(-s) | ||
| ISetDelayed(HurwitzLerchPhi(C0,s_,a_), | ||
| Power(a,Negate(s))), | ||
| // HurwitzLerchPhi(z_,1,1):=-Log(1-z)/z | ||
| ISetDelayed(HurwitzLerchPhi(z_,C1,C1), | ||
| Times(CN1,Power(z,CN1),Log(Subtract(C1,z)))), | ||
| // HurwitzLerchPhi(-1,s_,1):=(1-2^(1-s))*Zeta(s) | ||
| ISetDelayed(HurwitzLerchPhi(CN1,s_,C1), | ||
| Times(Subtract(C1,Power(C2,Subtract(C1,s))),Zeta(s))), | ||
| // HurwitzLerchPhi(0,1,a_):=1/a | ||
| ISetDelayed(HurwitzLerchPhi(C0,C1,a_), | ||
| Power(a,CN1)) | ||
| ); | ||
| } |
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| @@ -0,0 +1,10 @@ | ||
| { | ||
| HurwitzLerchPhi(0, 1, 1) = 1, | ||
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| HurwitzLerchPhi(z_, s_, 1) := PolyLog(s,z)/z, | ||
| HurwitzLerchPhi(z_, 0, a_) := 1/(1-z), | ||
| HurwitzLerchPhi(0, s_, a_) := a^(-s), | ||
| HurwitzLerchPhi(z_, 1, 1) := -Log(1-z)/z, | ||
| HurwitzLerchPhi(-1, s_, 1) := (1-2^(1-s))*Zeta(s), | ||
| HurwitzLerchPhi(0, 1, a_) := 1/a | ||
| } |
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| Original file line number | Diff line number | Diff line change |
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| @@ -1,4 +1,43 @@ | ||
| { | ||
| (* see http://www.reduce-algebra.com/docs/ztrans.pdf *) | ||
| ZTransform(a_^n_*f_,n_?NotListQ,z_?NotListQ):= ZTransform(f,n,z/a) | ||
| /; FreeQ(a,n)&&FreeQ(a,z), | ||
| ZTransform(n_*f_,n_?NotListQ,z_?NotListQ):= (-1)*z*D(ZTransform(f,n,z),z), | ||
| ZTransform(n_^2*f_,n_?NotListQ,z_?NotListQ):= z*D(ZTransform(f,n,z),z)+z^2*D(ZTransform(f,n,z),{z,2}), | ||
| ZTransform(n_^3*f_,n_?NotListQ,z_?NotListQ):= -z*D(ZTransform(f,n,z),z)-3*z^2*D(ZTransform(f,n,z),{z,2})-z^3*D(ZTransform(f,n,z),{z,3}), | ||
| (* ZTransform(n_^k_Integer*f_,n_?NotListQ,z_?NotListQ):=(-1)*z*D(ZTransform(n^(k-1)*f,n,z),z) | ||
| /; k>0, | ||
| *) | ||
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| ZTransform(a_^n_ ,n_?NotListQ,z_?NotListQ):=z/(z-a) | ||
| /; FreeQ(a,n)&&FreeQ(a,z) | ||
| /; FreeQ(a,n)&&FreeQ(a,z), | ||
| ZTransform(a_^(f_*n_) ,n_?NotListQ,z_?NotListQ):=z/(z-a^f) | ||
| /; FreeQ({a,f},n)&&FreeQ({a,f},z), | ||
| ZTransform(f_./(n_+g_),n_?NotListQ,z_?NotListQ):=f*HurwitzLerchPhi(1/z, 1, g) | ||
| /; FreeQ({f,g},n)&&FreeQ({f,g},z), | ||
| ZTransform((n_!)^(-1),n_?NotListQ,z_?NotListQ):=(E^(1/z)) | ||
| /; FreeQ({f,g},n)&&FreeQ({f,g},z) , | ||
| ZTransform(f_./(g_.*n_!),n_?NotListQ,z_?NotListQ):=(E^(1/z)*f)/g | ||
| /; FreeQ({f,g},n)&&FreeQ({f,g},z), | ||
| ZTransform(f_./(2*n_+1)!,n_?NotListQ,z_?NotListQ):=Sqrt(z)*f*Sinh(1/Sqrt(z)) | ||
| /; FreeQ(f,n)&&FreeQ(f,z), | ||
| ZTransform(Cos(f_.*n_)/(n_)!,n_?NotListQ,z_?NotListQ):=E^(Cos(f)/z)*Cos(Sin(f)/z) | ||
| /; FreeQ(f,n)&&FreeQ(f,z), | ||
| ZTransform(Sin(f_.*n_)/(n_)!,n_?NotListQ,z_?NotListQ):=E^(Cos(f)/z)*Sin(Sin(f)/z) | ||
| /; FreeQ(f,n)&&FreeQ(f,z), | ||
| ZTransform(Cos(f_.*(n_+1))/(n_+1),n_?NotListQ,z_?NotListQ):=(1/2)*z*(-Log((E^(I*f)-1/z)/E^(I*f))-Log(1-E^(I*f)/z)) | ||
| /; FreeQ(f,n)&&FreeQ(f,z), | ||
| ZTransform(Sin(f_.*(n_+1))/(n_+1),n_?NotListQ,z_?NotListQ):=(-(1/2))*I*z*(Log((E^(I*f)-1/z)/E^(I*f))-Log(1 - E^(I*f)/z)) | ||
| /; FreeQ(f,n)&&FreeQ(f,z), | ||
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| ZTransform(Cos(f_.*n_+t_.),n_?NotListQ,z_?NotListQ):=(z*(-Cos(f-t)+z*Cos(t)))/(1+z^2-2*z*Cos(f)) | ||
| /; FreeQ({f,t},n)&&FreeQ({f,t},z), | ||
| ZTransform(Cosh(f_.*n_+t_.),n_?NotListQ,z_?NotListQ):=(z*(-Cosh(f-t) + z*Cosh(t)))/(1 + z^2 - 2*z*Cosh(f)) | ||
| /; FreeQ({f,t},n)&&FreeQ({f,t},z), | ||
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| ZTransform(Sin(f_.*n_+t_.),n_?NotListQ,z_?NotListQ):=(z*(Sin(f-t)+z*Sin(t)))/(1 +z^2-2*z*Cos(f)) | ||
| /; FreeQ({f,t},n)&&FreeQ({f,t},z), | ||
| ZTransform(Sinh(f_.*n_+t_.),n_?NotListQ,z_?NotListQ):=(z*(Sinh(f-t)+ z*Sinh(t)))/(1+z^2-2*z*Cosh(f)) | ||
| /; FreeQ({f,t},n)&&FreeQ({f,t},z) | ||
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| } |