Nuprl Definition : sine-approx
sine-approx(x;k;N) ==
eval u = poly-approx(λi.(r(if (i rem 2 =z 0) then 1 else -1 fi ))/((2 * i) + 1)!;x^2;k;2 * N) in
eval b = |u| + 1 in
eval z = x b in
(u * z) ÷ 4 * b
Definitions occuring in Statement :
poly-approx: poly-approx(a;x;k;N),
rnexp: x^k1,
int-rdiv: (a)/k1,
int-to-real: r(n),
fact: (n)!,
absval: |i|,
callbyvalue: callbyvalue,
ifthenelse: if b then t else f fi ,
eq_int: (i =z j),
apply: f a,
lambda: λx.A[x],
remainder: n rem m,
divide: n ÷ m,
multiply: n * m,
add: n + m,
minus: -n,
natural_number: $n
Definitions occuring in definition :
poly-approx: poly-approx(a;x;k;N),
lambda: λx.A[x],
int-rdiv: (a)/k1,
int-to-real: r(n),
ifthenelse: if b then t else f fi ,
eq_int: (i =z j),
remainder: n rem m,
minus: -n,
fact: (n)!,
rnexp: x^k1,
add: n + m,
absval: |i|,
callbyvalue: callbyvalue,
apply: f a,
divide: n ÷ m,
multiply: n * m,
natural_number: $n
FDL editor aliases :
sine-approx
Latex:
sine-approx(x;k;N) ==
eval u = poly-approx(\mlambda{}i.(r(if (i rem 2 =\msubz{} 0) then 1 else -1 fi ))/((2 * i) + 1)!;x\^{}2;k;2 * N) in
eval b = |u| + 1 in
eval z = x b in
(u * z) \mdiv{} 4 * b
Date html generated:
2019_10_29-AM-10_31_00
Last ObjectModification:
2019_01_30-PM-01_29_42
Theory : reals
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