Exit[]

<<Sigma.m

<<PLDESolver.m

Example 1

re=(1+n)^2 (2+n) f[2+n] (n S[-1,n]+(-1)^n S[1,n])+(1+n)(2+n) f[n] (2 (-1)^n+(-1)^n n-S[-1,n]-2 n S[-1,n]-n^2 S[-1,n]+(-1)^n S[1,n]+(-1)^n n S[1,n])+(1+n) (2+n) f[1+n] (2 (-1)^n+(-1)^n n-S[-1,n]-n S[-1,n]+2 (-1)^n S[1,n]+2 (-1)^n n S[1,n]);
rhs=(2+n)^2-2 (-1)^n (1+n)^3 S[-1,n]-(-1-n) S[1,n];

SolvePLDE[re==rhs,f[n]]

Example 2

aL={-n (-5-(((I))^(Underscript[n, .]))+2 n (((I))^(Underscript[n, .]))) (1+S[1,n]+n S[1,n]) (3+2 n+2 S[1,n]+3 n S[1,n]+(n^2) S[1,n]),-2 (1+n) (2+3 n-2 (((I))^(Underscript[n, .]))+n (((I))^(Underscript[n, .]))) S[1,n] (3+2 n+2 S[1,n]+3 n S[1,n]+(n^2) S[1,n]),(1+n) (2+n) (8+n-8 (((I))^(Underscript[n, .]))-3 n (((I))^(Underscript[n, .]))+2 (n^2) (((I))^(Underscript[n, .]))) S[1,n] (1+S[1,n]+n S[1,n])};

fL={-(((I))^(Underscript[n, .])) (15 (n^3)+10 (n^4)-(64+12 I) S[1,n]-(168+62 I) n S[1,n]-(164+126 I) (n^2) S[1,n]-(49+126 I) (n^3) S[1,n]+(25-62 I) (n^4) S[1,n]+(14-12 I) (n^5) S[1,n]-(64+8 I) ((S[1,n])^2)-(232+48 I) n ((S[1,n])^2)-(332+118 I) (n^2) ((S[1,n])^2)-(228+152 I) (n^3) ((S[1,n])^2)-(64+108 I) (n^4) ((S[1,n])^2)+(4-40 I) (n^5) ((S[1,n])^2)+(4-6 I) (n^6) ((S[1,n])^2))-((((((I))^(Underscript[n, .]))))^2) (3 (n^3)-4 (n^4)-4 (n^5)+(64+12 I) S[1,n]+(184+38 I) n S[1,n]+(188+38 I) (n^2) S[1,n]+(75+6 I) (n^3) S[1,n]-(9+10 I) (n^4) S[1,n]-(24+4 I) (n^5) S[1,n]-8 (n^6) S[1,n]+(64+8 I) ((S[1,n])^2)+(248+32 I) n ((S[1,n])^2)+(372+46 I) (n^2) ((S[1,n])^2)+(260+24 I) (n^3) ((S[1,n])^2)+(64-4 I) (n^4) ((S[1,n])^2)-(24+8 I) (n^5) ((S[1,n])^2)-(20+2 I) (n^6) ((S[1,n])^2)-4 (n^7) ((S[1,n])^2))+((1/4)-(I/4)) ((((((I))^(Underscript[n, .]))))^3) ((-6+9 I) (n^4)-(7-3 I) (n^5)-(2+2 I) (n^6)-(12+140 I) S[1,n]-(78+478 I) n S[1,n]-(164+660 I) (n^2) S[1,n]-(156+468 I) (n^3) S[1,n]-(78+157 I) (n^4) S[1,n]-(28+5 I) (n^5) S[1,n]-(10-4 I) (n^6) S[1,n]-(2+2 I) (n^7) S[1,n]-(8+136 I) ((S[1,n])^2)-(64+592 I) n ((S[1,n])^2)-(170+1066 I) (n^2) ((S[1,n])^2)-(210+1018 I) (n^3) ((S[1,n])^2)-(128+534 I) (n^4) ((S[1,n])^2)-(33+129 I) (n^5) ((S[1,n])^2)+2 I (n^6) ((S[1,n])^2)+(1+5 I) (n^7) ((S[1,n])^2))-((1/4)+(I/4)) (((I))^(Underscript[n, .])) ((9+6 I) (n^4)+(3+7 I) (n^5)-(2-2 I) (n^6)-(116+12 I) S[1,n]-(354+46 I) n S[1,n]-(396+100 I) (n^2) S[1,n]-(172+140 I) (n^3) S[1,n]+(27-106 I) (n^4) S[1,n]+(55-32 I) (n^5) S[1,n]+(12+2 I) (n^6) S[1,n]-(2-2 I) (n^7) S[1,n]-(120+8 I) ((S[1,n])^2)-(496+32 I) n ((S[1,n])^2)-(822+74 I) (n^2) ((S[1,n])^2)-(678+130 I) (n^3) ((S[1,n])^2)-(254+152 I) (n^4) ((S[1,n])^2)+(7-103 I) (n^5) ((S[1,n])^2)+(38-36 I) (n^6) ((S[1,n])^2)+(9-5 I) (n^7) ((S[1,n])^2))-((1/4)+(I/4)) ((6-9 I) (n^4)+(7-3 I) (n^5)+(2+2 I) (n^6)-(12+116 I) S[1,n]-(78+354 I) n S[1,n]-(164+396 I) (n^2) S[1,n]-(156+172 I) (n^3) S[1,n]-(58+3 I) (n^4) S[1,n]+(14+17 I) (n^5) S[1,n]+(18+10 I) (n^6) S[1,n]+(4+4 I) (n^7) S[1,n]-(8+120 I) ((S[1,n])^2)-(64+496 I) n ((S[1,n])^2)-(170+822 I) (n^2) ((S[1,n])^2)-(210+678 I) (n^3) ((S[1,n])^2)-(120+266 I) (n^4) ((S[1,n])^2)-(9+19 I) (n^5) ((S[1,n])^2)+(26+24 I) (n^6) ((S[1,n])^2)+(13+11 I) (n^7) ((S[1,n])^2)+(2+2 I) (n^8) ((S[1,n])^2))+((1/4)+(I/4)) ((((((I))^(Underscript[n, .]))))^2) ((6-9 I) (n^4)+(7-3 I) (n^5)+(2+2 I) (n^6)+(12-140 I) S[1,n]+(46-478 I) n S[1,n]+(100-660 I) (n^2) S[1,n]+(140-468 I) (n^3) S[1,n]+(126-187 I) (n^4) S[1,n]+(74-43 I) (n^5) S[1,n]+(26+2 I) (n^6) S[1,n]+(4+4 I) (n^7) S[1,n]+(8-136 I) ((S[1,n])^2)+(32-592 I) n ((S[1,n])^2)+(74-1066 I) (n^2) ((S[1,n])^2)+(130-1018 I) (n^3) ((S[1,n])^2)+(160-546 I) (n^4) ((S[1,n])^2)+(127-155 I) (n^5) ((S[1,n])^2)+(62-12 I) (n^6) ((S[1,n])^2)+(17+7 I) (n^7) ((S[1,n])^2)+(2+2 I) (n^8) ((S[1,n])^2)),(-(1/4)+(I/4)) ((((((I))^(Underscript[n, .]))))^3) ((-6+9 I) (n^4)-(7-3 I) (n^5)-(2+2 I) (n^6)-(12+140 I) S[1,n]-(78+478 I) n S[1,n]-(164+660 I) (n^2) S[1,n]-(156+468 I) (n^3) S[1,n]-(78+157 I) (n^4) S[1,n]-(28+5 I) (n^5) S[1,n]-(10-4 I) (n^6) S[1,n]-(2+2 I) (n^7) S[1,n]-(8+136 I) ((S[1,n])^2)-(64+592 I) n ((S[1,n])^2)-(170+1066 I) (n^2) ((S[1,n])^2)-(210+1018 I) (n^3) ((S[1,n])^2)-(128+534 I) (n^4) ((S[1,n])^2)-(33+129 I) (n^5) ((S[1,n])^2)+2 I (n^6) ((S[1,n])^2)+(1+5 I) (n^7) ((S[1,n])^2))+((1/4)+(I/4)) (((I))^(Underscript[n, .])) ((9+6 I) (n^4)+(3+7 I) (n^5)-(2-2 I) (n^6)-(116+12 I) S[1,n]-(354+46 I) n S[1,n]-(396+100 I) (n^2) S[1,n]-(172+140 I) (n^3) S[1,n]+(27-106 I) (n^4) S[1,n]+(55-32 I) (n^5) S[1,n]+(12+2 I) (n^6) S[1,n]-(2-2 I) (n^7) S[1,n]-(120+8 I) ((S[1,n])^2)-(496+32 I) n ((S[1,n])^2)-(822+74 I) (n^2) ((S[1,n])^2)-(678+130 I) (n^3) ((S[1,n])^2)-(254+152 I) (n^4) ((S[1,n])^2)+(7-103 I) (n^5) ((S[1,n])^2)+(38-36 I) (n^6) ((S[1,n])^2)+(9-5 I) (n^7) ((S[1,n])^2))+((1/4)+(I/4)) ((6-9 I) (n^4)+(7-3 I) (n^5)+(2+2 I) (n^6)-(12+116 I) S[1,n]-(78+354 I) n S[1,n]-(164+396 I) (n^2) S[1,n]-(156+172 I) (n^3) S[1,n]-(58+3 I) (n^4) S[1,n]+(14+17 I) (n^5) S[1,n]+(18+10 I) (n^6) S[1,n]+(4+4 I) (n^7) S[1,n]-(8+120 I) ((S[1,n])^2)-(64+496 I) n ((S[1,n])^2)-(170+822 I) (n^2) ((S[1,n])^2)-(210+678 I) (n^3) ((S[1,n])^2)-(120+266 I) (n^4) ((S[1,n])^2)-(9+19 I) (n^5) ((S[1,n])^2)+(26+24 I) (n^6) ((S[1,n])^2)+(13+11 I) (n^7) ((S[1,n])^2)+(2+2 I) (n^8) ((S[1,n])^2))-((1/4)+(I/4)) ((((((I))^(Underscript[n, .]))))^2) ((6-9 I) (n^4)+(7-3 I) (n^5)+(2+2 I) (n^6)+(12-140 I) S[1,n]+(46-478 I) n S[1,n]+(100-660 I) (n^2) S[1,n]+(140-468 I) (n^3) S[1,n]+(126-187 I) (n^4) S[1,n]+(74-43 I) (n^5) S[1,n]+(26+2 I) (n^6) S[1,n]+(4+4 I) (n^7) S[1,n]+(8-136 I) ((S[1,n])^2)+(32-592 I) n ((S[1,n])^2)+(74-1066 I) (n^2) ((S[1,n])^2)+(130-1018 I) (n^3) ((S[1,n])^2)+(160-546 I) (n^4) ((S[1,n])^2)+(127-155 I) (n^5) ((S[1,n])^2)+(62-12 I) (n^6) ((S[1,n])^2)+(17+7 I) (n^7) ((S[1,n])^2)+(2+2 I) (n^8) ((S[1,n])^2))-(((I))^(Underscript[n, .])) (15 (n^5)+10 (n^6)-(256+12 I) S[1,n]-(928+86 I) n S[1,n]-(1392+262 I) (n^2) S[1,n]-(1120+440 I) (n^3) S[1,n]-(520+440 I) (n^4) S[1,n]-(113+262 I) (n^5) S[1,n]+(21-86 I) (n^6) S[1,n]+(14-12 I) (n^7) S[1,n]-(256+8 I) ((S[1,n])^2)-(1184+64 I) n ((S[1,n])^2)-(2320+222 I) (n^2) ((S[1,n])^2)-(2512+436 I) (n^3) ((S[1,n])^2)-(1640+530 I) (n^4) ((S[1,n])^2)-(648+408 I) (n^5) ((S[1,n])^2)-(132+194 I) (n^6) ((S[1,n])^2)-52 I (n^7) ((S[1,n])^2)+(4-6 I) (n^8) ((S[1,n])^2))-((((((I))^(Underscript[n, .]))))^2) (3 (n^5)-4 (n^6)-4 (n^7)+(256+12 I) S[1,n]+(992+62 I) n S[1,n]+(1552+126 I) (n^2) S[1,n]+(1216+120 I) (n^3) S[1,n]+(440+40 I) (n^4) S[1,n]+(3-18 I) (n^5) S[1,n]-(61+18 I) (n^6) S[1,n]-(32+4 I) (n^7) S[1,n]-8 (n^8) S[1,n]+(256+8 I) ((S[1,n])^2)+(1248+48 I) n ((S[1,n])^2)+(2544+118 I) (n^2) ((S[1,n])^2)+(2768+148 I) (n^3) ((S[1,n])^2)+(1656+90 I) (n^4) ((S[1,n])^2)+(440+8 I) (n^5) ((S[1,n])^2)-(60+22 I) (n^6) ((S[1,n])^2)-(84+12 I) (n^7) ((S[1,n])^2)-(28+2 I) (n^8) ((S[1,n])^2)-4 (n^9) ((S[1,n])^2)),((1/4)-(I/4)) ((((((I))^(Underscript[n, .]))))^3) ((-6+9 I) (n^4)-(7-3 I) (n^5)-(2+2 I) (n^6)-(12+140 I) S[1,n]-(78+478 I) n S[1,n]-(164+660 I) (n^2) S[1,n]-(156+468 I) (n^3) S[1,n]-(78+157 I) (n^4) S[1,n]-(28+5 I) (n^5) S[1,n]-(10-4 I) (n^6) S[1,n]-(2+2 I) (n^7) S[1,n]-(8+136 I) ((S[1,n])^2)-(64+592 I) n ((S[1,n])^2)-(170+1066 I) (n^2) ((S[1,n])^2)-(210+1018 I) (n^3) ((S[1,n])^2)-(128+534 I) (n^4) ((S[1,n])^2)-(33+129 I) (n^5) ((S[1,n])^2)+2 I (n^6) ((S[1,n])^2)+(1+5 I) (n^7) ((S[1,n])^2))-((1/4)+(I/4)) (((I))^(Underscript[n, .])) ((9+6 I) (n^4)+(3+7 I) (n^5)-(2-2 I) (n^6)-(116+12 I) S[1,n]-(354+46 I) n S[1,n]-(396+100 I) (n^2) S[1,n]-(172+140 I) (n^3) S[1,n]+(27-106 I) (n^4) S[1,n]+(55-32 I) (n^5) S[1,n]+(12+2 I) (n^6) S[1,n]-(2-2 I) (n^7) S[1,n]-(120+8 I) ((S[1,n])^2)-(496+32 I) n ((S[1,n])^2)-(822+74 I) (n^2) ((S[1,n])^2)-(678+130 I) (n^3) ((S[1,n])^2)-(254+152 I) (n^4) ((S[1,n])^2)+(7-103 I) (n^5) ((S[1,n])^2)+(38-36 I) (n^6) ((S[1,n])^2)+(9-5 I) (n^7) ((S[1,n])^2))-((1/4)+(I/4)) ((6-9 I) (n^4)+(7-3 I) (n^5)+(2+2 I) (n^6)-(12+116 I) S[1,n]-(78+354 I) n S[1,n]-(164+396 I) (n^2) S[1,n]-(156+172 I) (n^3) S[1,n]-(58+3 I) (n^4) S[1,n]+(14+17 I) (n^5) S[1,n]+(18+10 I) (n^6) S[1,n]+(4+4 I) (n^7) S[1,n]-(8+120 I) ((S[1,n])^2)-(64+496 I) n ((S[1,n])^2)-(170+822 I) (n^2) ((S[1,n])^2)-(210+678 I) (n^3) ((S[1,n])^2)-(120+266 I) (n^4) ((S[1,n])^2)-(9+19 I) (n^5) ((S[1,n])^2)+(26+24 I) (n^6) ((S[1,n])^2)+(13+11 I) (n^7) ((S[1,n])^2)+(2+2 I) (n^8) ((S[1,n])^2))+((1/4)+(I/4)) ((((((I))^(Underscript[n, .]))))^2) ((6-9 I) (n^4)+(7-3 I) (n^5)+(2+2 I) (n^6)+(12-140 I) S[1,n]+(46-478 I) n S[1,n]+(100-660 I) (n^2) S[1,n]+(140-468 I) (n^3) S[1,n]+(126-187 I) (n^4) S[1,n]+(74-43 I) (n^5) S[1,n]+(26+2 I) (n^6) S[1,n]+(4+4 I) (n^7) S[1,n]+(8-136 I) ((S[1,n])^2)+(32-592 I) n ((S[1,n])^2)+(74-1066 I) (n^2) ((S[1,n])^2)+(130-1018 I) (n^3) ((S[1,n])^2)+(160-546 I) (n^4) ((S[1,n])^2)+(127-155 I) (n^5) ((S[1,n])^2)+(62-12 I) (n^6) ((S[1,n])^2)+(17+7 I) (n^7) ((S[1,n])^2)+(2+2 I) (n^8) ((S[1,n])^2)),n};

SolvePLDE[aL,fL,n]

Example 3

re=(1+n) f[n]+(-3-2 n) f[1+n]+(2+n) f[2+n];
rhs=-I (Sqrt[3]) ((((E^((2 I π)/3))))^n);

SolvePLDE[re==rhs,f[n]]

SolvePLDE[re==rhs,f[n],Tower->{(Underoverscript[(∑^(.)), ((Subscript[ι, 1])=1), n])(1/(Subscript[ι, 1]))}]

SolvePLDE[re==rhs,f[n],Tower->{(Underoverscript[(∑^(.)), ((Subscript[ι, 1])=1), n])(1/(Subscript[ι, 1])),(Underoverscript[(∑^(.)), ((Subscript[ι, 1])=1), n])(( (((I(I+(Sqrt[3]))))^(Underscript[(Subscript[ι, 1]), .])))/((Subscript[ι, 1]) (2^(Underscript[(Subscript[ι, 1]), .]))))}]

Example 4

re=(1+n) (2+n) (8-8 (((-1))^n)+n-3 (((-1))^n) n+2 (((-1))^n) (n^2)) f[2+n] S[1,n] (1+S[1,n]+n S[1,n])-2 (1+n) (2-2 (((-1))^n)+3 n+(((-1))^n) n) f[1+n] S[1,n] (3+2 n+2 S[1,n]+3 n S[1,n]+(n^2) S[1,n])-n (-5+(((-1))^(1+n))+2 (((-1))^n) n) f[n] (1+S[1,n]+n S[1,n]) (3+2 n+2 S[1,n]+3 n S[1,n]+(n^2) S[1,n]);
rhs=(12 (3+2 n)-12 (((-1))^n) (1+n) (3+2 n)) S[1,n]+(12 (1+n) (5+3 n)-12 (((-1))^n) (((1+n))^2) (5+3 n)) ((S[1,n])^2)+(12 (((1+n))^2) (2+n)-12 (((-1))^n) (((1+n))^3) (2+n)) ((S[1,n])^3);

SolvePLDE[re==rhs,f[n]]

Example 5

re=-(1+(((-1))^n)) (1+n) (1+2 n) f[1+n] S[1,n] (3+2 n+2 S[1,n]+3 n S[1,n]+(n^2) S[1,n]) (15+16 n+4 (n^2)+8 S[1,n]+12 n S[1,n]+4 (n^2) S[1,n])+(1+n) (((2+n))^2) f[2+n] S[1,n] (1+S[1,n]+n S[1,n]) (1+(((-1))^n)+4 n+4 (((-1))^n) n+4 (n^2)+4 (((-1))^n) (n^2)+4 S[1,n]-2 (((-1))^n) S[1,n]+4 n S[1,n]+6 (((-1))^n) n S[1,n]+16 (((-1))^n) (n^2) S[1,n]+8 (((-1))^n) (n^3) S[1,n])+f[n] (-1-S[1,n]-n S[1,n]) (3+2 n+2 S[1,n]+3 n S[1,n]+(n^2) S[1,n]) (-25+29 (((-1))^n)-45 n+63 (((-1))^n) n-24 (n^2)+48 (((-1))^n) (n^2)-4 (n^3)+12 (((-1))^n) (n^3)-16 S[1,n]+20 (((-1))^n) S[1,n]-40 n S[1,n]+62 (((-1))^n) n S[1,n]-32 (n^2) S[1,n]+74 (((-1))^n) (n^2) S[1,n]-8 (n^3) S[1,n]+40 (((-1))^n) (n^3) S[1,n]+8 (((-1))^n) (n^4) S[1,n]);
rhs=0;

SolvePLDE[re==rhs,f[n]]

Example 6

re=f[n]+((-1)^n+1)f[n+1]+f[n+2];
rhs=I^n;

SolvePLDE[re==rhs,f[n]]

Example 7

re=f[n]+((-1)^n+1)f[n+1]+f[n+2];
rhs=0;

SolvePLDE[re==rhs,f[n],Tower->{I^n}]

Example 8

re=f[n]+((-1)^n-1)f[n+1]+f[n+2];
rhs=I^n;

SolvePLDE[re==rhs,f[n]]

Example 9

re=f[n]+f[n+1]+((((-1))^(2/3))^n-1)f[n+2];
rhs=(((-1))^(1/3))^n;

SolvePLDE[re==rhs,f[n]]