Formula
Create this kind of graph to plot any explicit function in the form:
Parametric Y( u ) = f2(u, v), X( u ) = f1(u, v).
Polar R( u ) = f2(u, v), fi( u ) = f1(u, v), X=R*cos( fi ), Y=R*sin( fi ).
Cartesian Y( u ) = f2(u, v), X( u ) = u.
Click the button or select menu item <Data><Formula> to create this kind of graphs. This causes the Formula dialog box show, where you can modify properties of graph (formula, range of parameters u and v, color, width and so on). It is possible to draw families of lines with a given step of parameter v.
Notes:
- Only variable u and parameter v are possible in formula expression.
- Default value of parameter v is v=0.
- The set of operations and functions.
- When prompted to enter a formula the set of operations and functions you may use is the following.
Arithmetic operators:
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+
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a + b |
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-
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a - b |
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*
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a * b |
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/
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a / b |
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^
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a ^ b (a to the power of b) |
Important: In formula expression take a^b result in brackets.
For example, write exp(-((x-c)^2)) instead of exp(-(x-c)^2).
Built-in functions:
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sin(u)
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Sine, the angle 'u' must be in units of radians. |
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sind(u)
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Sine, the angle 'u' must be in units of degrees. |
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sinn(u,n)
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Sine of 2pi*n*u |
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cos(u)
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Cosine |
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cosd(u)
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Cosine, the angle 'u' must be in units of degrees. |
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cosn(u,n)
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Cosine of 2pi*n*u |
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hav(u)
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Haversine of u, hav(u) = (1-cos(u))/2 |
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havd(u)
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Haversine, the angle 'u' must be in units of degrees. |
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tan(u)
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Tangent |
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tand(u)
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Tangent, the angle 'u' must be in units of degrees. |
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sinc(u)
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Sine(u)/u |
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asin(u)
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Inverse sine |
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acos(u)
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Inverse cosine |
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atan(u)
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Inverse tangent |
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rad(u)
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Converts an angle measured in degrees to the equivalent number of radians. |
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exp(u)
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Exponent (i.e e to the power of u) |
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ln(u)
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Natural logarithm (base e) |
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log(u)
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Logarithm base 10 |
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pow(u, v)
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u to the power of v |
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sqrt(u)
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Square root |
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factorial(u)
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u!, if u value is not an integer, it is truncated. |
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sinh(u)
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Hyperbolic sine |
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cosh(u)
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Hyperbolic cosine |
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tanh(u)
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Hyperbolic tangent |
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asinh(u)
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Hyperbolic arc sine |
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acosh(u)
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Hyperbolic arc cosine |
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atanh(u)
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Hyperbolic arc tangent |
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besselj0(u)
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Bessel functions of the first kind: orders 0, 1, and n, respectively |
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besselj1(u)
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besseljn(u, n)
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bessely0(u)
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Bessel functions of the second kind: orders 0, 1, and n, respectively |
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bessely1(u)
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besselyn(u, n)
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The polynomials: orders 0, 1, and n, respectively |
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chebyshev(u,n)
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The Chebyshev polynomials of the first kind: 1, u, 2u^2-1, 4u^3-3u,... |
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legendre(u,n)
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The Legendre polynomials: 1, u, (3u^2-1)/2, (5u^3-3u)/2,... |
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laguerre(u,n)
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The Laguerre polynomials: 1, 1-u, (4u^2-4u+2)/2, (-u^3+9u^2-18u+6)/6,... |
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hermite(u,n)
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The Hermite polynomials: 1, 2u, 4u^2-2, 8u^3-12u,... |
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neumann(u,n)
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The Neumann polynomials: 1, 1/u, 1/u^2, (u^2+4)/u^3,... |
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gamma(u)
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Integral( x^(u-1)*exp(-x) ), with x limits from 0 to infinite |
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lngamma(u)
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The natural logarithm of gamma function |
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beta(u, v)
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Integral( x^(u-1)*(1-x)^(v-1) ) with x limits from 0 to 1 |
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