public final class TaylorSeries
extends java.lang.Object
Modifier and Type | Field and Description |
---|---|
static double |
FIVE_OVER_112
Constant value equal to 3/40.
|
static double |
HALF
Constant value equal to 1/2.
|
static double |
ONE_OVER_120
Constant value equal to 1/120 = 1/5!.
|
static double |
ONE_OVER_24
Constant value equal to 1/24 = 1/4!.
|
static double |
ONE_OVER_5040
Constant value equal to 1/5040 = 1/7!.
|
static double |
ONE_OVER_720
Constant value equal to 1/720 = 1/6!.
|
static double |
ONE_SIXTH
Constant value equal to 1/6 = 1/6.
|
static double |
ONE_THIRD
Constant value equal to 1/3.
|
static double |
Q_17_OVER_315
Constant value equal to 17/215.
|
static double |
THREE_OVER_40
Constant value equal to 3/40.
|
static double |
TWO_OVER_15
Constant value equal to 2/15.
|
Constructor and Description |
---|
TaylorSeries() |
Modifier and Type | Method and Description |
---|---|
static double |
asinO1(double x) |
static double |
asinO3(double x) |
static double |
asinO5(double x) |
static double |
asinO7(double x) |
static double |
cosO0(double a)
Returns the Taylor serie of the trigonometric cosine around a = 0 at the 0 order (constant).
|
static double |
cosO2(double a)
Returns the Taylor serie of the trigonometric cosine around a = 0 at the order of the 2nd degree.
|
static double |
cosO4(double a)
Returns the Taylor serie of the trigonometric cosine around a = 0 at the order of the 4th degree.
|
static double |
cosO6(double a)
Returns the Taylor serie of the trigonometric cosine around a = 0 at the order of the 6th degree.
|
static double |
sinO1(double a)
Returns the Taylor serie of the trigonometric sine around a = 0 at the order of the 1st degree.
|
static double |
sinO3(double a)
Returns the Taylor serie of the trigonometric sine around a = 0 at the order of the 3rd degree.
|
static double |
sinO5(double a)
Returns the Taylor serie of the trigonometric sine around a = 0 at the order of the 5th degree.
|
static double |
sinO7(double a)
Returns the Taylor serie of the trigonometric sine around a = 0 at the order of the 7th degree.
|
static double |
tanO1(double a)
Returns the Taylor serie of the trigonometric tan around a = 0 at the order of the 1st degree.
|
static double |
tanO3(double a)
Returns the Taylor serie of the trigonometric tan around a = 0 at the order of the 3rd degree.
|
static double |
tanO5(double a)
Returns the Taylor serie of the trigonometric tan around a = 0 at the order of the 5th degree.
|
static double |
tanO7(double a)
Returns the Taylor serie of the trigonometric tan around a = 0 at the order of the 7th degree.
|
public static final double HALF
public static final double ONE_THIRD
public static final double ONE_SIXTH
public static final double ONE_OVER_24
public static final double ONE_OVER_120
public static final double ONE_OVER_720
public static final double ONE_OVER_5040
public static final double TWO_OVER_15
public static final double THREE_OVER_40
public static final double FIVE_OVER_112
public static final double Q_17_OVER_315
public static final double cosO0(double a)
1
.
The error on this approximation is no more than |x|^2 / 2
, i.e. ~5e-17 if x = 1e-8.
We recall that the erro due to numercial approximation is 1e-16.a
- angle, in radianspublic static final double cosO2(double a)
1 - x^2/2
.
The error on this approximation is no more than |x|^4 / 4!
, i.e. ~4e-18 if x = 1e-4.a
- angle, in radianspublic static final double cosO4(double a)
1 - x^2/2 + x^4/4!
.
The error on this approximation is no more than |x|^6 / 6!
, i.e. ~1.3e-21 if x = 1e-3.a
- angle, in radianspublic static final double cosO6(double a)
1 - x^2/2 + x^4/4! - x^6/6!
.
The error on this approximation is no more than |x|^8 / 8!
, i.e. ~1.7e-20 if x = 1e-2.a
- angle, in radianspublic static final double sinO1(double a)
x
.
The error on this approximation is no more than |x|^3 / 3!
, i.e. ~1.6e-19 if x = 1e-6.a
- angle, in radianspublic static final double sinO3(double a)
x - x^3/3!
.
The error on this approximation is no more than |x|^5 / 120
, i.e. ~8.3e-18 if x = 1e-3.a
- angle, in radianspublic static final double sinO5(double a)
x - x^3/3! + x^5/5!
.
The error on this approximation is no more than |x|^7 / 7!
, i.e. ~2e-18 if x = 1e-2.a
- angle, in radianspublic static final double sinO7(double a)
x - x^3/3! + x^5/5! - x^7/7!
.
The error on this approximation is no more than |x|^9 / 9!
, i.e. ~2.8e-15 if x = 1e-1.a
- angle, in radianspublic static final double tanO1(double a)
x
.
The error on this approximation is no more than |x|^3 / 3
, i.e. ~4e-19 if x = 1e-6.a
- angle, in radianspublic static final double tanO3(double a)
x + x^3/3
.
The error on this approximation is no more than 2*|x|^5 / 15
, i.e. ~1.3e-21 if x = 1e-4.a
- angle, in radianspublic static final double tanO5(double a)
x + x^3/3 + 2x^5/15
.
The error on this approximation is no more than 17|x|^7 / 315
, i.e. ~5.4e-23 if x = 1e-3.a
- angle, in radianspublic static final double tanO7(double a)
x + x^3/3 + 2x^5/15 + 17x^7/315
.
The error on this approximation is no more than 62|x|^9 / 2835
, i.e. ~2.2e-20 if x = 1e-2.a
- angle, in radianspublic static final double asinO1(double x)
public static final double asinO3(double x)
public static final double asinO5(double x)
public static final double asinO7(double x)
Copyright © 2018 F.-X. Pineau, CDS, Observatoire Astronomique de Strasbourg, Universite de Strasbourg, CNRS. All Rights Reserved.