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Dataplot Vol 2 Vol 1

FERMDIRA

Name:
    FERMDIRA (LET)
Type:
    Library Function
Purpose:
    Compute the Fermi-Dirac function for orders -0.5, 0.5, 1.5, and 2.5.
Description:
    The Fermi-Dirac function of order -0.5 is defined as:

      FDM0P5(x) = [Int{0 to inf} t**(-1/2) / (1+exp(t-x)) dt]/ Gamma(1/2)

    The Fermi-Dirac function of order 0.5 is defined as:

      FDP0P5(x) = [Int{0 to inf} t**(1/2) / (1+exp(t-x)) dt]/ Gamma(3/2)

    The Fermi-Dirac function of order 1.5 is defined as:

      FDP1P5(x) = [Int{0 to inf} t**(3/2) / (1+exp(t-x)) dt]/ Gamma(5/2)

    The Fermi-Dirac function of order 2.5 is defined as:

      FDP2P5(x) = [Int{0 to inf} t**(5/2) / (1+exp(t-x)) dt]/ Gamma(7/2)

    where Gamma is the gamma function.

    If the specified order is within 0.1 of one of the supported orders, Dataplot will use the supported order. Otherwise, it returns an error message.

    Dataplot computes this function using ACM Algorithm 779 (see Reference: below). Specifically, it uses the routines FDM0P5, FDP0P5, FDP1P5, and FDP2P5.

Syntax:
    LET <y> = FERMDIRA(<x>,<ord>) <SUBSET/EXCEPT/FOR qualification>
    where <x> is a non-negative number, variable or parameter;
                  <ord> is a non-negative integer number, parameter, or variable containing one of -0.5, 0.5, 1.5, or 2.5;
                  <y> is a variable or a parameter (depending on what <x> and <ord> are) where the computed Fermi-Dirac function values are stored;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Examples:
    LET A = FERMDIRA(2.3,1.5)
    LET A = FERMDIRA(X,A1)
    LET X2 = FERMDIRA(X1,0.5) FOR X1 = -20 0.01 20
Default:
    None
Synonyms:
    None
Related Commands:
    ABRAM = Compute the Abramowitz integral.
    CLAUSN = Compute the Clausen integral.
    DEBYE = Compute the Debye function.
    EXP3 = Compute the cubic exponential integral.
    GOODST = Compute the Goodwin and Stanton integral.
    LOBACH = Compute the Lobachevski integral.
    SYNCH1 = Compute the synchrotron radiation function.
    SYNCH2 = Compute the synchrotron radiation function.
    STROM = Compute the Stromgren integral.
    TRAN = Compute the transport integral.
Reference:
    "ACM Transactions of Mathematical Software", Allan MacLead, Vol. xx, No. x, xx.
Applications:
    Special Functions
Implementation Date:
    2002/5
Program: 
    MULTIPLOT 2 2 
MULTIPLOT CORNER COORDINATES 5 5 95 95 
MULTIPLOT SCALE FACTOR 2
LET ORDER = -0.5 
TITLE ORDER = ^ORDER 
PLOT FERMDIRA(X,ORDER) FOR X = -10 0.1 50 
LET ORDER = 0.5 
TITLE ORDER = ^ORDER 
PLOT FERMDIRA(X,ORDER) FOR X = -10 0.1 50 
LET ORDER = 1.5 
TITLE ORDER = ^ORDER 
PLOT FERMDIRA(X,ORDER) FOR X = -10 0.1 50 
LET ORDER = 2.5 
TITLE ORDER = ^ORDER 
PLOT FERMDIRA(X,ORDER) FOR X = -10 0.1 50 
END OF MULTIPLOT 
MOVE 50 97 
JUSTIFICATION CENTER 
TEXT FERMI-DIRAC FUNCTIONS
    plot generated by sample program

Date created: 5/31/2002
Last updated: 4/4/2003
Please email comments on this WWW page to alan.heckert@nist.gov.