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!'二重ゼータ関数
OPTION BASE 0
LET KMAX=100000
DIM SS(KMAX)
INPUT A,B !' A>=2
FOR N=1 TO KMAX
LET SS(N)=SS(N-1)+1/N^B
NEXT N
FOR N=2 TO KMAX
LET S=S+1/N^A*SS(N-1)
NEXT N
PRINT S
END
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!'三重ゼータ関数
OPTION BASE 0
LET KMAX=100000
DIM SSS(KMAX),SS(KMAX)
INPUT A,B,C !' A>=2
FOR N=1 TO KMAX
LET SSS(N)=SSS(N-1)+1/N^C
NEXT N
FOR N=1 TO KMAX
LET SS(N)=SS(N-1)+1/N^B*SSS(N-1)
NEXT N
FOR N=2 TO KMAX
LET S=S+1/N^A*SS(N-1)
NEXT N
PRINT S
END
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!'四重ゼータ関数
OPTION BASE 0
LET KMAX=100000
DIM SSSS(KMAX),SSS(KMAX),SS(KMAX)
INPUT A,B,C,D !' A>=2
FOR N=1 TO KMAX
LET SSSS(N)=SSSS(N-1)+1/N^D
NEXT N
FOR N=1 TO KMAX
LET SSS(N)=SSS(N-1)+1/N^C*SSSS(N-1)
NEXT N
FOR N=1 TO KMAX
LET SS(N)=SS(N-1)+1/N^B*SSS(N-1)
NEXT N
FOR N=2 TO KMAX
LET S=S+1/N^A*SS(N-1)
NEXT N
PRINT S
END
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!'多重ゼータ関数
OPTION BASE 0
INPUT PROMPT "N=":N
LET KMAX=100000
DIM S(N,KMAX),A(N)
FOR I=1 TO N
INPUT PROMPT CHR$(64+I)&"=":A(I) !'A(1)>=2
NEXT I
FOR I=N TO 1 STEP -1
FOR J=1 TO KMAX
IF I<N THEN
LET S(I,J)=S(I,J-1)+1/J^A(I)*S(I+1,J-1)
ELSE
LET S(I,J)=S(I,J-1)+1/J^A(N)
END IF
NEXT J
NEXT I
PRINT S(1,KMAX)
END
ゼータ関数:ZETA(3)=1.20205690310973.. |ZETA(4)=1.08232323371114.. | ZETA(5)=1.03692775514334..
二重ゼータ関数: ZETA(2,1) |ZETA(3,1)+ZETA(2,2) | ZETA(4,1)+ZETA(3,2)+ZETA(2,3)
三重ゼータ関数: | ZETA(2,1,1) | ZETA(3,1,1)+ZETA(2,2,1)+ZETA(2,1,2)
四重ゼータ関数: | ZETA(2,1,1,1)
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