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sci_gsl >> sci_gsl > splfunc

splfunc

It computes the value of special functions e.g. Airy's function, Gamma function, Beta function, Bessel's function, Legendre's polynomial etc.

Syntax

y = splfunc(choice,c1,c2)

Parameters

y:

output

c1 and c2:

real or integer numbers depending on the type of special function to be evaluated.

choice:

It is used to choose the desired special function and is always a positive integer i.e. choice>0.

choice = 1:

Airy's Function Ai(x), c1 represents the x while c2 can be set to any value.

choice = 2:

Airy's Function Bi(x), c1 represents the x while c2 can be set to any value.

choice = 3:

Scaled Airy's Function Ai(x), c1 represents the x while c2 can be set to any value.

choice = 4:

Scaled Airy's Function Bi(x), c1 represents the x while c2 can be set to any value.

choice = 5:

Derivative of Airy's Function Ai(x), c1 represents the x while c2 can be set to any value.

choice = 6:

Derivative of Airy's Function Bi(x), c1 represents the x while c2 can be set to any value.

choice = 7:

Scaled Derivative of Airy's Function Ai(x), c1 represents the x while c2 can be set to any value.

choice = 8:

Scaled Derivative of Airy's Function Bi(x), c1 represents the x while c2 can be set to any value.

Choice = 9:

nth Zeros of Airy's Function Ai(x), c1 can be set to any value while c2 will be an integer representing nth zero.

choice = 10:

nth Zeros of Airy's Function Bi(x), c1 can be set to any value while c2 will be an integer representing nth zero.

choice = 11:

nth Zeros of Derivative of Airy's Function Ai(x), c1 can be set to any value while c2 will be an integer representing nth zero.

choice = 12:

nth Zeros of Derivative of Airy's Function Bi(x), c1 can be set to any value while c2 will be an integer representing nth zero.

choice = 13:

Regular Cylindrical Bessel's Function Jn(x), c1 represents x and c2 represents n. Here n is an integer.

choice = 14:

Iregular Cylindrical Bessel's Function Yn(x), c1 represents x, x>0 and c2 represents n. Here n is greater than equal to 0.

choice = 15:

Regular Modified Cylindrical Bessel's Function In(x), c1 represents x, x>0 and c2 represents n. Here n is greater than equal to 0.

choice = 16:

Scaled Regular Modified Cylindrical Bessel's Function In(x), c1 represents x, x>0 and c2 represents n. Here n is an integer.

choice = 17:

Iregular Modified Cylindrical Bessel's Function Kn(x), c1 represents x, x>0 and c2 represents n. Here n is an integer.

Choice = 18:

Scaled Iregular Modified Cylindrical Bessel's Function Kn(x), c1 represents x, x>0 and c2 represents n. Here n is an integer.

choice = 19:

Regular Spherical Bessel's Function jl(x), c1 and c2 represent x and l respectively. x is real and l is an integer. x and l both are greater than equal to zero.

choice = 20:

Iregular Spherical Bessel's Function yl(x), c1 and c2 represent x and l respectively. x is real and l is an integer. x and l both are greater than equal to zero.

choice = 21:

Scaled Regular Modified Spherical Bessel's Function il(x), c1 and c2 represent x and l respectively. x is real and l is an integer. x and l both are greater than equal to zero.

choice = 22:

Scaled Iregular Modified Spherical Bessel's Function kl(x), c1 and c2 represent x and l respectively. x is real and l is an integer. x and l both are greater than equal to zero.

choice = 23:

Regular Cylindrical Bessel's Function Jn(x), c1 represents x, x>0 and c2 represents n. Here n is a fraction.

choice = 24:

Irregular Cylindrical Bessel's Function Yn(x), c1 represents x, x>0 and c2 represents n. Here n is a fraction.

choice = 25:

Regular Modified Cylindrical Bessel's Function In(x), c1 represents x, x>0 and c2 represents n. Here n is a fraction, n>0

choice = 26:

Scaled Regular Modified Cylindrical Bessel's Function In(x), c1 represents x, x>0 and c2 represents n. Here n is a fraction, n>0

Choice = 27:

Iregular Modified Cylindrical Bessel's Function Kn(x), c1 represents x, x>0 and c2 represents n. Here n is a fraction, n>0

choice = 28:

Scaled Iregular Modified Cylindrical Bessel's Function Kn(x), c1 represents x, x>0 and c2 represents n. Here n is a fraction, n>0

choice = 29:

nth Zero of Regular Cylindrical Bessel Function J0(x), c1 can be set to any value while c2 represents n and is a positive integer.

choice = 30:

nth Zero of Regular Cylindrical Bessel Function J1(x), c1 can be set to any value while c2 represents n and is a positive integer.

choice = 31:

mth Zero of Regular Cylindrical Bessel Function Jn(x), c1 represents m while c2 represents n. Here n is a positive fraction.

choice = 32:

Dawson Function or Integral Da(x), c1 represents x while c2 can be set to any value.

choice = 33:

Debye Function or Integral of first order D1(x), c1 represents x and x>0 while c2 can be set to any value.

choice = 34:

Debye Function or Integral of second order D2(x), c1 represents x and x>0 while c2 can be set to any value.

choice = 35:

Error Function erf(x), c1 represents x and x>0 while c2 can be set to any value.

Choice = 36:

Complementary Error Function erfc(x), c1 represents x and x>0 while c2 can be set to any value.

Choice = 37:

Log Complementary Error Function erfc_ln(x), c1 represents x and x>0 while c2 can be set to any value.

choice = 38:

Normalized Normal or Gaussian Probability Density Function N~(0,1), c1 represents x while c2 can be set to any value.

choice = 39:

Upper tail Normalized Gaussian probability density function N~(0,1), c1 represents x while c2 can be set to any value.

choice = 40:

Real part of the Exponential Integral En(x), c1 and c2 represent x and n respectively. n is positive real number.

choice = 41:

Fermi Dirac Integral Fn(x), c1 represents x and x is real number while c2 represents n and n is positive integer.

choice = 42:

Gamma Function, c1 represents n and can be set to an integer or fraction. c1 cannot be set equal to zero and c2 can be set to any value

choice = 43:

Beta function, c1 and c2 represent m and n. Both m and n are positive integers.

choice = 44:

Laguerre Polynomial of order n Ln(x), c1 and c2 represent x and n respectively. n is a non-negative integer.

choice = 45:

Legendre's Polynomial of order n Pn(x), c1 and c2 represent x and n respectively. n is a non-negative integer.

Description

This function takes the parameters choice and two numbers to calculate the special functions.

Examples

// Beta Function
choice=43
c1=1
c2=2
y = splfunc(choice,c1,c2)

Authors


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