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    $B:8JU$N(B |$B!A(B| $B$O%Y%/%H%k$ND9$5!$1&JU$N$=$l$Oa || $B$H$9$k$3$H$b$"$j$^$9!%(B $B$^$?!$Fb@Q$O(B (a ,b) $B$J$I$HI=$9$3$H$b$"$j$^$9!%(B
    $B%A%'%S%7%'%U(B (Chebyshev) $B$NITEy<0(B
    a $B!e(B b$B!$(Bc $B!e(B d $B$N$H$-(B
    (a + b)(c + d) $B!e(B 2(a c + b d).
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    $B%A%'%S%7%'%U(B (Chebyshev) $B$NB?9`<0(B
    $BBh0l Tn (cos$B&H(B) = cos(n$B&H(B).
    $BBhFs Un(cos$B&H(B) = sin[(n +1)$B&H(B] / sin$B&H(B.
    $B;03Q4X?t(B
    $B2CK!DjM}(B
    sin($B&A(B+$B&B(B) = sin$B&A(B cos$B&B(B + cos$B&A(B sin $B&B(B,
    cos($B&A(B+$B&B(B) = cos$B&A(B cos$B&B(B - sin$B&A(B sin $B&B(B.
    $B%X%m%s(B (Heron) $B$N8x<0(B
    $B;03Q7A$NLL@Q(B$B$r(B S$B!$;0JU$ND9$5$r(B a, b, c $B$H$9$k$H(B
    S = $B"e(B(s (s - a) (s - b) (s - c)).
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    $B;X?t4X?t!$BP?t4X?t(B
    $BDj5A(B
    y = b x $B"N(B x = logb y. ($B$3$3$G(B 0 < b $B!b(B1, y > 0)
    $B;X?t4X?t(B
    b x+y = b x b y $B$^$?$O(B exp (x + y) = exp x exp y.
    $BBP?t4X?t(B
    log (x y) = log x + log y.
    $BDl$O!$<+L@$J>l9g$^$?$O2?$G$b$$$$>l9g!$N,$9$3$H$b$"$j$^$9!%(B $B0lHL$K!$?tCM7W;;(B(10$B?JK!(B)$B$NJ8L.$G$O(B 10$B!$Hy@QJ,$NJ8L.$G$O(B e$B!$(B $B>pJs=hM}(B(2$B?JK!(B)$B$NJ8L.$G$O(B 2 $B$H2r10$B"a(Blog ($B>oMQBP?t(B) $B$H$7$F!$(B loge$B"a(Bln ($B<+A3BP?t(B)$B!$(B log2$B"a(Blg (2$B?JBP?t(B)$B$HI=$9$3$H$b$"$j$^$9!%(B
    $BJ#AG?t(B
    $B%I!&%b%"%V%k(B (de Moivre) $B$NDjM}(B
    (cos$B&H(B + i sin$B&H(B)n = cos n$B&H(B + i sin n$B&H(B.
    $B%*%$%i!<(B (Euler) $B$NDjM}(B
    e i x = cos x + i sin x.
    $B?tNs(B
    $BEyHf?tNs$NItJ,OB(B
    r$B!b(B1 $B$N$H$-(B 1 + r + r 2 + $B!D(B + r n-1 =
    1 - r n
    1 - r
    .
    $B<+A3?t$NItJ,OB(B
    n
    $B&2(B
    k =1
    k =
    1
    2
    n (n + 1).
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    n
    $B&2(B
    k =1
    k 2 =
    1
    6
    n (n + 1) (2 n + 1).
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    n
    $B&2(B
    k =1
    k 3 = {
    1
    2
    n (n + 1)}2.
    $B<+A3?t$N(Bm$B>hOB(B
    n
    $B&2(B
    k =1
    k m =
    1
    m+1
    m
    $B&2(B
    j =0
    m+1Cj bj nm+1-j.
    $B$3$3$G!$(B{bj} $B$O(B m
    $B&2(B
    j =0
    m+1Cj bj =m+1 ( m=0,1,2,$B!D(B) $B$GDj5A$5$l$k?tNs!%(B
    $B$J$*!$(Bb1$B$NId9f$rJQ$($?$b$N$,(B $B%Y%k%L!<%$(B (Bernoulli) $B?t(B {Bj} $B$G!$(B $B;X?t4X?t7?$NJl4X?t(B
    $B!g(B
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    j =0
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    x j
    j!
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    x
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    .
    $B$^$?$O!$Fs9`78?t$H!VD>8r!W$9$k$h$&$JA22=<0(B
    B0=1, m
    $B&2(B
    j =0
    m+1Cj Bj =0 ( m=1,2,$B!D(B)
    $B$GDj5A$5$l$^$9!%6qBNE*$J?tCM$O(B
    j0 12345 678910 1112131415 16171819202122
    Bj1
    -
    1
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    0
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    66
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    3617
    510
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    43867
    798
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    330
    0
    854513
    138
    $B=gNs!&AH$_9g$o$;(B
    $B=gNs(B
    nPr =
    n!
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    .
    $B=EJ#=gNs(B
    n$B&0(Br = n r.
    $BNc(B $BH,75(B ($B$O$C$1(B)*7$B$N(B 8 $B$O(B 23$B!%(B
    $BAH$_9g$o$;(B
    nCr =
    n!
    (n - r)! r!
    . nCn-r = nCr $B!$(B nCr = n-1Cr-1 + n-1Cr.
    2$B9`DjM}(B
    (a + b)n = n
    $B&2(B
    r =0
    nCr a n-r b r.
    $B=EJ#AH$_9g$o$;(B
    nHr = n+r-1Cr.
    #{(x1 , $B!D(B , xn) | x1 + $B!D(B + xn = r , 0$B!e(B x1 , $B!D(B , xn$B":(BZ } = nHr.
    $B%+%?%i%s(B (Catalan) $B?t(B
    Cn =
    1
    n +1
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    $B&2(B
    r =1
    Cr-1Cn-r.
    $BNc(B 1 $BFL(B n+2 $B3Q7A$r(B n-1 $BK\$NBP3Q@~$G(B n $B8D$N;03Q7A$KJ,3d$9$k;EJ}$N?t!%(B
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    $B%9%?!<%j%s%0(B (Stirling) $B?t(B
    $BBh0l s (n, r ) n $BMWAG$NCV49$N$&$A%5%$%/%k(B ($B=d2sCV49(B) $B$N?t$,(B r $B8D$N$b$N(B
    s (n, r ) = (n - 1) s (n - 1, r ) + s (n -1, r - 1 ),
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    x(n ) = (-1)n s (n, 0) + (-1)n -1 s (n, 1) x + (-1)n -2 s (n, 2) x2 + $B!D(B + s (n, n ) xn.
    $BBhFs S (n, r ) n $BMWAG$N=89g$r(B r $B8D$N%V%m%C%/$KJ,$1$k;EJ}$N?t(B
    S (n, r ) = r S (n - 1, r ) + S (n -1, r - 1 ),
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    xn = S (n, 0) + S (n, 1) x(1) + S (n, 2) x(2) + $B!D(B + S (n, n ) x(n ).
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    ($BCm(B2) $B5-9f$b$$$/$D$+$"$j!$Nc$($P(B Knuth $B$NK\(B$B$G$O(B $BBh0l
    ($BCm(B3) $BBh0l
    ($BCm(B4) $B8;;a9a(B$B$N?t$OBhFsS (5, r) = 52 (= 54 - 2).
    $B?tI=(B
    $BFs9`78?t(B $B%9%?!<%j%s%0?t(B
    $B%Q%9%+%k(B (Pascal) $B$N(B3$B3Q7A(B $BBh0l $BBhFs
         1       
        1 1      
       1 2 1     
      1 3 3 1    
     1 4 6 4 1   
    
    $B&2(B=20
    $B&2(B=21
    $B&2(B=22
    $B&2(B=23
    $B&2(B=24
    
     1               
     0  1            
     0  1  1         
     0  2  3  1      
     0  6 11  6  1   
     0 24 50 35 10 1 
    
    $B&2(B=0!
    $B&2(B=1!
    $B&2(B=2!
    $B&2(B=3!
    $B&2(B=4!
    $B&2(B=5!
    
      1              
      0 1            
      0 1  1         
      0 1  3  1      
      0 1  7  6  1   
      0 1 15 25 10 1 
    
    $B&2(B=B(0)= 1
    $B&2(B=B(1)= 1
    $B&2(B=B(2)= 2
    $B&2(B=B(3)= 5
    $B&2(B=B(4)=15
    $B&2(B=B(5)=52
    
    ($BCm(B1) B $B$O%Y%k(B (Bell) $B?t!%(B
    $B3NN(!&E}7W(B
    $B2CK!DjM}(B
    P(A$B"@(BB) = P(A) + P(B) - P(A$B"A(BB).
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    P(A) P(B | A) = P(B) P(A | B) = P(A$B"A(BB).
    $BFC$K;v>](BA$B$H(BB$B$,FHN)$J>l9g!$(B P(A) P(B) = P(A$B"A(BB).
    $BJ?6QCM!$4|BTCM(B
    m =
    1
    n
    n
    $B&2(B
    k =1
    xk.
    E(X) = $B&2(B
    k
    xk pk. (X $B$O3NN(JQ?t$G(B $B&2(B
    k
    pk = 1)
    $BJ,;6(B
    V =
    1
    n
    n
    $B&2(B
    k =1
    (xk - m)2 =
    1
    n
    n
    $B&2(B
    k =1
    xk2 - m2.
    V(X) = E(X2) -{E(X)}2.
    $BI8=`JP:9(B
    $B&R(B = $B"e(BV.
    $B9TNs!$9TNs<0(B
    $B@5J}9TNs(B A $B$N9TNs<0$O(B | A | $B$^$?$O(B det A $B$GI=$7$^$9!%(B $B$^$?!$E>CV9TNs$O(B tA $B$GI=$7$^$9!%(B
    $B9TNs$N@Q(B
    (ai j) (bi j) = ( n
    $B&2(B
    k =1
    ai k bk j).


    a11a12
    a21a22




    b11b12
    b21b22


    =


    a11b11+ a12b21 a11b12+ a12b22
    a21b11+ a22b21 a21b12+ a22b22


    .
    $B%5%i%9(B (Sarrus) $B$N8x<0(B
    a b c
    d e f
    g h i
    = a e i + d h c + g f b - c e g - f h a - i d b.
    $B9TNs$NM>0x;R(B
    n $BA $B$N(B i $B9T$H(B j $BNs$r=|$$$?(B n-1 $BAi j $B$GI=$9$3$H$K$9$k$H(B
    | A | = n
    $B&2(B
    j =1
    (-1)i + j ai j | Ai j |.
    $B$3$3$G(B (-1)i + j | Ai j | = ãi j $B$r(B ai j $B$NM>0x;R!$(B t(ãi j) = Ã $B$rM>0x;R9TNs$H$$$$(B
    A Ã = | A | E.
    (E $B$OC10L9TNs!%(B| A | $B!b(B 0 $B$J$i$P(B A-1 = Ã / | A |$B!%(B)
    $B%V%i%&%6$K$h$C$F!H(B~$B!I$,I=<($5$l$J$$2DG=@-$,$"$k$N$G!$@.J,$4$H$K=q$/$H(B
    (ai j) ( (-1)i + j | Aj i | ) =| A | ($B&D(Bi j).
    $B%/%i%a!<%k(B (Cramer) $B$N8x<0(B


    A x = b, | A | $B!b(B 0 $B"M(B xj =
    j
    det (a1 ,$B!D(B, b ,$B!D(B, an)
    | A |


    .
    $B%U%!%s%G%k%b%s%I(B (Vandermonde) $B$N9TNs<0(B
    11$B!D(B1
    x1x2 $B!D(Bxn
    $B!'(B$B!'(B$B!D(B$B!'(B
    x1n-1 x2n-1 $B!D(Bxnn-1
    =
    $B&0(B
    i > j
    (xi - xj).
    $BJ#AG9TNs(B
    tA $B$NJ#AG6&Lr9TNs$r(B A* $B$GI=$9(B (tA = A*) $B$3$H$K$9$k$H(B (R $B$G$O(BA* = tA)
    A* tA = A A* = A tA = -A A* = -A A*A = E det A $B!b(B 0 A*A = AA*
    C $B?oH<(B $BBP>N(B Hermite $B8rBe(B $BOD(BHermite unitary $B@5B'(B $B@55,(B
    R $BE>CV(B $BN(B $BODBP>N(B $BD>8r(B
    $B9TNs$N$J$972(B
    Mn(C ) $B$r(B C $B$NMWAG$r@.J,$H$9$k(Bn$B
    n $B$B!'(B GLn(C ) = {A$B":(BMn(C ) | det A $B!b(B 0 }
    n $B$B!'(B SLn(C ) = {A$B":(BMn(C ) | det A = 1 }
    n $B$B!'(B Un(C ) = {A$B":(BMn(C ) | A*A = E }
    n $B8r72(B$B!'(B On(R ) = {A$B":(BMn(R ) | tAA = E }
    $B$H$9$k$H(B SLn(C )$B!$(B Un(C )$B!$(B On(R ) $B$O(B GLn(C ) $B$NItJ,72!%$^$?!$(B


    cos $B&H(B-sin $B&H(B
    sin $B&H(Bcos $B&H(B


    $B":(B O2(R ).
    $BHyJ,!&@QJ,(B
    [$B1&$+$i$N(B]$B6K8BCM$NDj5A(B ($B&E(B-$B&DO@K!(B)
    limx$B"*(Ba+0 f (x) = A $B"N(B $B"O&E(B> 0 $B"P&D(B> 0 (0 < x - a <$B&D(B $B"M(B | f (x) - A | <$B&E(B).
    $B<+A3BP?t$NDl(B
    e = limx$B"*(B0 (1 + x)1 / x = limx$B"*!^!g(B (1 + 1 / x)x = 1 + 1 / 1! + 1 / 2! + 1 / 3! + $B!D(B $B"b(B 2.71828.
    $B@Q!$9g@.4X?t!$5U4X?t$NHyJ,(B
    (f g)' = f 'g + f g '.
    {f (g (x))}' = f '(g (x)) g '(x).
    y = f (x) $B"M(B (f -1)'(y) = 1 / f '(x).
    $BM-M}4X?t!$;03Q4X?t!$;X?t4X?t!$BP?t4X?t$NHyJ,(B
    (xn)' = n x n-1 (n $B$O (sin x)' = cos x $B!$(B (cos x)' = -sin x $B!$(B (tan x)' = 1 / cos2 x $B!$(B
    (a x)' = a x log a $B!$(B (loga x)' = 1 / (x log a).
    $BITDj@QJ,(B
    $B"i(B
    dx
    x
    = log |x| + C.
    $B"i(B
    dx
    x 2 + 1
    = tan-1 x + C.
    $BItJ,@QJ,(B
    $B"i(B f (x) g ' (x) dx = f (x) g (x) -$B"i(B f ' (x) g (x) dx.
    $BDj@QJ,(B
    F '(x) = f (x) $B$N$H$-(B (F (x) $B$,(B f (x) $B$N86;O4X?t$N$H$-(B)
    $B"i(Bab f (x) dx = [F (x)]ab = F (b) - F (a).
    $BCV49@QJ,(B
    p (b)
    $B"i(Bf (x) dx =
    p (a)
    b
    $B"i(Bf (p (t)) p' (t) dt.
    a
    2$B=E@QJ,$K$*$1$kJQ?tJQ49(B
    p : W $B"*(B R 2 $B$r(B C 1-$B
    $B"j(Bp (D) f (x,y) dx dy = $B"j(BD f (x (u,v), y (u,v)) | Jp | du dv.
    $B$3$3$G(B Jp $B$O(B p $B$N%d%3%S%"%s(B (Jacobian) $B$G(B
    Jp =
    $B"_(B(x, y)
    $B"_(B(u, v)
    =
    $B"_(Bx
    $B"_(Bu
    $B"_(Bx
    $B"_(Bv
    $B"_(By
    $B"_(Bu
    $B"_(By
    $B"_(Bv
    .
    $B%Y!<%?4X?t$H%,%s%^4X?t(B
    $B&"(B( p, q) = $B"i(B01 x p-1(1-x)q-1dx,
    $B&#(B(s) = $B"i(B0$B!g(B e-x xs-1dx.
    $BN>p, q) = $B&#(B( p)$B&#(B(q) /$B&#(B( p+q) $B$G$D$J$,$C$F$$$k!%(B
    n $B$,HsIi$N@0?t$N>l9g(B $B&#(B( n+1) = n $B&#(B( n) = $B!D(B = n! $B$J$N$G(B
    1
    $B"i(B
    0
    t m(1-t)ndt =
    m!n!
    (m+n+1)!
    .
    $B$^$?!$(Bx = $B&A(B+($B&B(B-$B&A(B) t$B$H$$$&CV49@QJ,$K$h$j(B
    $B&B(B
    $B"i(B
    $B&A(B
    (x-$B&A(B)m($B&B(B-x)ndx =
    m!n!
    (m+n+1)!
    ($B&B(B-$B&A(B)m+n+1.
    $B%0%j!<%s(B (Green) $B$NDjM}(B
    $B"i(B$B"_(BD (f dx + g dy) = $B"j(BD (-$B"_(Bf /$B"_(By +$B"_(Bg /$B"_(Bx) dx dy.
    $B%9%H!<%/%9(B (Stokes) $B$NDjM}(B
    $B"i(B$B"_(BD$B&X(B = $B"i(BD d$B&X(B.
    $B%Y%/%H%k2r@O(B
    $B%J%V%i(B (nabla) *8 $B1i;;;R$NDj5A(B
    $B"`(B = ($B"_(B/$B"_(Bx,$B"_(B/$B"_(By,$B"_(B/$B"_(Bz) = ex$B"_(B/$B"_(Bx + ey$B"_(B/$B"_(By + ez$B"_(B/$B"_(Bz.
    df = grad f = $B"`(Bf.
    div A = $B"`!&(BA.
    rot A = curl A = $B"`!_(BA.
    $B%i%W%i%7%"%s(B (Laplacian) $B$NDj5A(B
    $B&$(B = $B"_(B2/$B"_(Bx2 + $B"_(B2/$B"_(By2 + $B"_(B2/$B"_(Bz2 =$B"`!&"`(B.

    (*1) $B?t3X$G$OB>$K
  15. $B%i%F%sJ8;z(B($B%m!<%^;z(B)$B$NBgJ8;z$NI.5-BN(B
    Euler Script
  16. $B%i%F%sJ8;z$N>.J8;z$HBgJ8;z$N(B $B5l%I%$%D8l%U%)%s%H(B
    Euler Fraktur lowercase Euler Fraktur uppercase
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