Parametric graphs

Create this kind of graph to plot any explicit function in the form:

Click the button Formula  or select menu item <Data><Formula> to create this kind of graphs. This will cause 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:

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:

+
a + b
-
a - b
*
a * b
/
a / b
^
a ^ b (a to the power of b)

Built-in functions:

sin(u)
Sine, the angle 'u' must be in units of radians.
sind(u)
Sine, the angle 'u' must be in units of degrees.
sinn(u,n)
Sine of 2pi*n*u
cos(u)
Cosine
cosd(u)
Cosine, the angle 'u' must be in units of degrees.
cosn(u,n)
Cosine of 2pi*n*u
hav(u)
Haversine of u, hav(u) = (1-cos(u))/2
havd(u)
Haversine, the angle 'u' must be in units of degrees.
tan(u)
Tangent
tand(u)
Tangent, the angle 'u' must be in units of degrees.
sinc(u)
Sine(u)/u

asin(u)
Inverse sine
acos(u)
Inverse cosine
atan(u)
Inverse tangent

rad(u)
Converts an angle measured in degrees to the equivalent number of radians.

exp(u)
Exponent (i.e e to the power of u)
ln(u)
Natural logarithm (base e)
log(u)
Logarithm base 10
pow(u, v)
u to the power of v
sqrt(u)
Square root
factorial(u)
u!, if u value is not an integer, it is truncated.

sinh(u)
Hyperbolic sine
cosh(u)
Hyperbolic cosine
tanh(u)
Hyperbolic tangent
asinh(u)
Hyperbolic arc sine
acosh(u)
Hyperbolic arc cosine
atanh(u)
Hyperbolic arc tangent

besselj0(u)
Bessel functions of the first kind: orders 0, 1, and n, respectively
besselj1(u)
besseljn(u, n)
bessely0(u)
Bessel functions of the second kind: orders 0, 1, and n, respectively
bessely1(u)
besselyn(u, n)

 
The polynomials: orders 0, 1, and n, respectively
chebyshev(u,n)
The Chebyshev polynomials of the first kind: 1, u, 2u^2-1, 4u^3-3u,...
legendre(u,n)
The Legendre polynomials: 1, u, (3u^2-1)/2, (5u^3-3u)/2,...
laguerre(u,n)
The Laguerre polynomials: 1, 1-u, (4u^2-4u+2)/2, (-u^3+9u^2-18u+6)/6,...
hermite(u,n)
The Hermite polynomials: 1, 2u, 4u^2-2, 8u^3-12u,...
neumann(u,n)
The Neumann polynomials: 1, 1/u, 1/u^2, (u^2+4)/u^3,...

gamma(u)
Integral( x^(u-1)*exp(-x) ), with x limits from 0 to infinite
lngamma(u)
The natural logarithm of gamma function
beta(u, v)
Integral( x^(u-1)*(1-x)^(v-1) ) with x limits from 0 to 1
normal(u, v)
exp( -u*u/4/v/v )/v/sqrt(2*pi)
normln(u, v)
exp( -ln(u)*ln(u)/4/v/v )/v/sqrt(2*pi)
normalsum(u)
Returns the area under the Gaussian probability density function, integrated from minus infinity to u.

expdist(u, v)
v*exp(-v*u)
expdistc(u, v)
1 - exp(-v*u)
The formula is the integral from 0 to u value of expdist(u, v).
poison(u, v)
exp(-v)*v^u/u!, if u value is not an integer, it is truncated.
poissonfirst(u, v)
Returns the sum of the first v terms of the Poisson distribution.
poissonlast(u, v)
Returns the sum of the terms v+1 to infinity of the Poisson distribution.

erf(u)
The error function ERF(u).
erfc(u)
The complementary error function returns the complementary ERF function integrated between u and infinity.
chisqleft(u, v)
Returns the area under the left hand tail (from 0 to u) of the Chi square probability density function with v degrees of freedom.
chisqright(u, v)
Returns the area under the right hand tail (from u to infinity) of the Chi square probability density function with v degrees of freedom.

fisher(u)
0.5*ln((1+u)/(1-u)), the Fisher transformation at u
fisheri(u)
(exp(2u) - 1)/(exp(2u) + 1), the inverse Fisher transformation

abs(u)
Absolute value
int(u)
Integer part of u
max(u,v)
Maximum of u and v
min(u,v)
Minimum of u and v

ceil(u)
Returns the smallest integer that is greater than or equal to u.
floor(u)
Returns the largest integer that is less than or equal to u.
round(u)
Returns the value of the argument u rounded to the nearest int value.
fmod(u,v)
Calculates the floating-point remainder f of u / v such that u = i * v + f, where i is an integer.
hypot(u,v)
Calculates the expression sqrt(u*u + v*v).

sign(u)
Sign of u. If u is less than 0, the value of the function is -1. If u is equal to 0, the value of the function is 0. If u is greater than 0, the value of the function is 1.
step(u,v)
Step function. If u is less than v, the value of the function is 0. If u is greater than or equal to v, the value of the function is 1. If you need a function which is 1 up to a certain value and then 0 beyond that value, use the expression step(v,u).
equal(u,v)
If u is equal to v, the value of the function is 1, else 0
equalzero(u)
If u is equal to 0, the value of the function is 1, else 0
ltzero(u)
If u is less than 0, the value of the function is 1, else 0
gtzero(u)
If u is greater than 0, the value of the function is 1, else 0

random(u)
Random number generator, generates a random floating point number such that 0 ≤ Result < u

effect(u, v)
(1 + u/v)^v - 1, financial function.
u is the nominal interest rate,
v is the number of compounding periods per year.

Predefined constants:

pi
3.141592654
e
2.718281828

See example.


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