XProfan

English

p.specht

The Gammafunktion is known under many others properties The kontinuierliche Variante the Faktoriellenfunktion - z.B. is facto(5)=5*4*3*2*1. The Gammafunktion gamma(x+1) ought to with ganzzahligem reellen Input the same Result supplying How facto(x), and so a (differenzierbare) Formel for Kurvenform the Faktoriellenfunktion supplying. the works but yet not so correctly.: numerous berühmte Näherungen existieren. These stammt from 2007 and becomes in the nachstehenden Program ausgetestet and your absolute deviation determined.

Compile Mark Separation

Window Title " Test the Gammafunktions-Näherung to [G.Nemes 2007]"
Window Style 24:Window 0,0-800,%maxy-40:font 2
'https://en.wikipedia.org/wiki/Stirling%27s_approximation#A_convergent_version_of_Stirling's_formula

proc GammaNemes :parameters z!

    case z!<1/1e4:return 0:if z!>168:print " *** OVERFLOW ERROR ***":return 0:endif
    var uz!=1/z!
    return Sqrt(6.2831853071795865*uz!)*(.367879441171442322*(z!+1/(12*z!-.1*uz!)))^z!

endproc

proc facto :parameters x&

    case x&<1:return 0

    if x&>168:print " *** OVERFLOW ERROR ***":return 0:endif

        var p!=1

        whileloop x&,1,-1

            p!=p!*&Loop

        endwhile

        return p!

    Endproc

    'Main part
    Declare gamma!
    CLS:set("decimals",4)

    Whileloop 180

        gamma!=GammaNemes(&Loop+1)
        Print:print " ",&Loop,
        print stature$("%g",facto(&Loop)),
        print stature$("%g",round(gamma!,4)),
        print " AbsErr: ";stature$("%g",gamma!-facto(&Loop))
        waitinput 8000
        case %csrlin>34:cls

    endwhile

    print "---"
    waitinput
    End