OpenMath Content Dictionary: kelvin

Canonical URL:
http://www.openmath.org/CDs/kelvin.ocd
CD File:
kelvin.ocd
CD as XML Encoded OpenMath:
kelvin.omcd
Defines:
KelvinBei, KelvinBer, KelvinHei, KelvinHer, KelvinKei, KelvinKer
Date:
23/8/2001
Version:
(Revision )
Review Date:
Status:
private
Uses CD:
arith1, bessel, nums1, relation1, transc1

1/1/5000

This content dictionary contains symbols to describe the kelvin functions.


KelvinBer

KelvinBer This symbol takes two arguments, it represents a solution of the equations: KelvinBer(v,x) + I*KelvinBei(v,x) = BesselJ(v,x*exp(3*I*Pi/4)) and KelvinBer(v,x) - I*KelvinBei(v,x) = BesselJ(v,x*exp(-3*I*Pi/4))

Commented Mathematical property (CMP):
KelvinBer(v,x) + I*KelvinBei(v,x) = BesselJ(v,x*exp(3*I*Pi/4))
Formal Mathematical property (FMP):
<OMOBJ>
      <OMA><OMS cd="relation1" name="eq"/>
        <OMA><OMS cd="arith1" name="plus"/>
          <OMA><OMS cd="kelvin" name="KelvinBer"/>
            <OMV name="nu"/>
            <OMV name="x"/>
          </OMA>
          <OMA><OMS cd="arith1" name="times"/>
            <OMS cd="nums1" name="i"/>
            <OMA><OMS cd="kelvin" name="KelvinBei"/>
              <OMV name="nu"/>
              <OMV name="x"/>
            </OMA>
          </OMA>
        </OMA>
        <OMA><OMS cd="bessel" name="BesselJ"/>
          <OMV name="nu"/>
          <OMA><OMS cd="arith1" name="times"/>
            <OMV name="x"/>
            <OMA><OMS cd="transc1" name="exp"/>
              <OMA><OMS cd="arith1" name="times"/>
                <OMI>3</OMI>
                <OMS cd="nums1" name="i"/>
                <OMA>
                  <OMS cd="arith1" name="divide"/>
                  <OMS cd="nums1" name="pi"/><OMI>4</OMI>
                </OMA>
              </OMA>
            </OMA>
          </OMA>
        </OMA>
      </OMA>
    </OMOBJ>

eq (plus (KelvinBer ( nu, x) , times (i, KelvinBei ( nu, x) ) ) , BesselJ ( nu, times ( x, exp (times (3, i, divide (pi, 4) ) ) ) ) )

Commented Mathematical property (CMP):
KelvinBer(v,x) - I*KelvinBei(v,x) = BesselJ(v,x*exp(-3*I*Pi/4))
Formal Mathematical property (FMP):
<OMOBJ>
      <OMA><OMS cd="relation1" name="eq"/>
        <OMA><OMS cd="arith1" name="minus"/>
          <OMA><OMS cd="kelvin" name="KelvinBer"/>
              <OMV name="nu"/>
              <OMV name="x"/>
          </OMA>
          <OMA><OMS cd="arith1" name="times"/>
            <OMS cd="nums1" name="i"/>
            <OMA><OMS cd="kelvin" name="KelvinBei"/>
              <OMV name="nu"/>
              <OMV name="x"/>
            </OMA>
          </OMA>
        </OMA>
        <OMA><OMS cd="bessel" name="BesselJ"/>
          <OMV name="nu"/>
          <OMA><OMS cd="arith1" name="times"/>
            <OMV name="x"/>
            <OMA><OMS cd="transc1" name="exp"/>
              <OMA><OMS cd="arith1" name="times"/>
                <OMA><OMS cd="arith1" name="unary_minus"/>
                  <OMI>3</OMI>
                </OMA>
                <OMS cd="nums1" name="i"/>
                <OMA>
                  <OMS cd="arith1" name="divide"/>
                  <OMS cd="nums1" name="pi"/><OMI>4</OMI>
                </OMA>
              </OMA>
            </OMA>
          </OMA>
        </OMA>
      </OMA>
    </OMOBJ>

eq (minus (KelvinBer ( nu, x) , times (i, KelvinBei ( nu, x) ) ) , BesselJ ( nu, times ( x, exp (times (unary_minus (3) , i, divide (pi, 4) ) ) ) ) )

Signatures:
sts


[Next: KelvinBei] [Last: KelvinHei] [Top]

KelvinBei

KelvinBei This symbol takes two arguments, it represents a solution of the equations: KelvinBer(v,x) + I*KelvinBei(v,x) = BesselJ(v,x*exp(3*I*Pi/4)) and KelvinBer(v,x) - I*KelvinBei(v,x) = BesselJ(v,x*exp(-3*I*Pi/4))

Commented Mathematical property (CMP):
KelvinBer(v,x) + I*KelvinBei(v,x) = BesselJ(v,x*exp(3*I*Pi/4))
Formal Mathematical property (FMP):
<OMOBJ>
      <OMA><OMS cd="relation1" name="eq"/>
        <OMA><OMS cd="arith1" name="plus"/>
          <OMA><OMS cd="kelvin" name="KelvinBer"/>
            <OMV name="nu"/>
            <OMV name="x"/>
          </OMA>
          <OMA><OMS cd="arith1" name="times"/>
            <OMS cd="nums1" name="i"/>
            <OMA><OMS cd="kelvin" name="KelvinBei"/>
              <OMV name="nu"/>
              <OMV name="x"/>
            </OMA>
          </OMA>
        </OMA>
        <OMA><OMS cd="bessel" name="BesselJ"/>
          <OMV name="nu"/>
          <OMA><OMS cd="arith1" name="times"/>
            <OMV name="x"/>
            <OMA><OMS cd="transc1" name="exp"/>
              <OMA><OMS cd="arith1" name="times"/>
                <OMI>3</OMI>
                <OMS cd="nums1" name="i"/>
                <OMA>
                  <OMS cd="arith1" name="divide"/>
                  <OMS cd="nums1" name="pi"/><OMI>4</OMI>
                </OMA>
              </OMA>
            </OMA>
          </OMA>
        </OMA>
      </OMA>
    </OMOBJ>

eq (plus (KelvinBer ( nu, x) , times (i, KelvinBei ( nu, x) ) ) , BesselJ ( nu, times ( x, exp (times (3, i, divide (pi, 4) ) ) ) ) )

Commented Mathematical property (CMP):
KelvinBer(v,x) - I*KelvinBei(v,x) = BesselJ(v,x*exp(-3*I*Pi/4))
Formal Mathematical property (FMP):
<OMOBJ>
      <OMA><OMS cd="relation1" name="eq"/>
        <OMA><OMS cd="arith1" name="minus"/>
          <OMA><OMS cd="kelvin" name="KelvinBer"/>
            <OMV name="nu"/>
            <OMV name="x"/>
          </OMA>
          <OMA><OMS cd="arith1" name="times"/>
            <OMS cd="nums1" name="i"/>
            <OMA><OMS cd="kelvin" name="KelvinBei"/>
              <OMV name="nu"/>
              <OMV name="x"/>
            </OMA>
          </OMA>
        </OMA>
        <OMA><OMS cd="bessel" name="BesselJ"/>
          <OMV name="nu"/>
          <OMA><OMS cd="arith1" name="times"/>
            <OMV name="x"/>
            <OMA><OMS cd="transc1" name="exp"/>
              <OMA><OMS cd="arith1" name="times"/>
                <OMA><OMS cd="arith1" name="unary_minus"/>
                  <OMI>3</OMI>
                </OMA>
                <OMS cd="nums1" name="i"/>
                <OMA>
                  <OMS cd="arith1" name="divide"/>
                  <OMS cd="nums1" name="pi"/><OMI>4</OMI>
                </OMA>
              </OMA>
            </OMA>
          </OMA>
        </OMA>
      </OMA>
    </OMOBJ>

eq (minus (KelvinBer ( nu, x) , times (i, KelvinBei ( nu, x) ) ) , BesselJ ( nu, times ( x, exp (times (unary_minus (3) , i, divide (pi, 4) ) ) ) ) )

Signatures:
sts


[Next: KelvinKer] [Previous: KelvinBer] [Top]

KelvinKer

KelvinKer This symbol takes two arguments, it represents a solution of the equations: KelvinKer(v,x) + I*KelvinKei(v,x) = exp(-v*Pi*I/2)*BesselK(v,x*exp(I*Pi/4)) and KelvinKer(v,x) - I*KelvinKei(v,x) = exp(-v*Pi*I/2)*BesselK(v,x*exp(-I*Pi/4))

Commented Mathematical property (CMP):
KelvinKer(v,x) + I*KelvinKei(v,x) = exp(-v*Pi*I/2)*BesselK(v,x*exp(I*Pi/4))
Formal Mathematical property (FMP):
<OMOBJ>
      <OMA><OMS cd="relation1" name="eq"/>
        <OMA><OMS cd="arith1" name="plus"/>
          <OMA><OMS cd="kelvin" name="KelvinKer"/>
            <OMV name="nu"/>
            <OMV name="x"/>
          </OMA>
          <OMA><OMS cd="arith1" name="times"/>
            <OMS cd="nums1" name="i"/>
            <OMA><OMS cd="kelvin" name="KelvinKei"/>
              <OMV name="nu"/>
              <OMV name="x"/>
            </OMA>
          </OMA>
        </OMA>
        <OMA><OMS cd="arith1" name="times"/>
          <OMA><OMS cd="transc1" name="exp"/>
            <OMA><OMS cd="arith1" name="times"/>
              <OMA><OMS cd="arith1" name="unary_minus"/>
                <OMV name="nu"/>
              </OMA>
              <OMS cd="nums1" name="i"/>
              <OMA><OMS cd="arith1" name="divide"/>
                <OMS cd="nums1" name="pi"/><OMI>2</OMI>
              </OMA>
            </OMA>
          </OMA>
          <OMA><OMS cd="bessel" name="BesselK"/>
            <OMV name="nu"/>
            <OMA><OMS cd="arith1" name="times"/>
              <OMV name="x"/>
              <OMA><OMS cd="transc1" name="exp"/>
                <OMA><OMS cd="arith1" name="times"/>
                  <OMI>3</OMI>
                  <OMS cd="nums1" name="i"/>
                  <OMA>
                    <OMS cd="arith1" name="divide"/>
                    <OMS cd="nums1" name="pi"/><OMI>4</OMI>
                  </OMA>
                </OMA>
              </OMA>
            </OMA>
          </OMA>
        </OMA>
      </OMA>
    </OMOBJ>

eq (plus (KelvinKer ( nu, x) , times (i, KelvinKei ( nu, x) ) ) , times (exp (times (unary_minus ( nu) , i, divide (pi, 2) ) ) , BesselK ( nu, times ( x, exp (times (3, i, divide (pi, 4) ) ) ) ) ) )

Commented Mathematical property (CMP):
KelvinKer(v,x) - I*KelvinKei(v,x) = exp(-v*Pi*I/2)*BesselK(v,x*exp(-I*Pi/4))
Formal Mathematical property (FMP):
<OMOBJ>
      <OMA><OMS cd="relation1" name="eq"/>
        <OMA><OMS cd="arith1" name="minus"/>
          <OMA><OMS cd="kelvin" name="KelvinKer"/>
            <OMV name="nu"/>
            <OMV name="x"/>
          </OMA>
          <OMA><OMS cd="arith1" name="times"/>
            <OMS cd="nums1" name="i"/>
            <OMA><OMS cd="kelvin" name="KelvinKei"/>
              <OMV name="nu"/>
              <OMV name="x"/>
            </OMA>
          </OMA>
        </OMA>
        <OMA><OMS cd="arith1" name="times"/>
          <OMA><OMS cd="transc1" name="exp"/>
            <OMA><OMS cd="arith1" name="times"/>
              <OMA><OMS cd="arith1" name="unary_minus"/>
                <OMV name="nu"/>
              </OMA>
              <OMS cd="nums1" name="i"/>
              <OMA><OMS cd="arith1" name="divide"/>
                <OMS cd="nums1" name="pi"/><OMI>2</OMI>
              </OMA>
            </OMA>
          </OMA>
          <OMA><OMS cd="bessel" name="BesselK"/>
            <OMV name="nu"/>
            <OMA><OMS cd="arith1" name="times"/>
              <OMV name="x"/>
              <OMA><OMS cd="transc1" name="exp"/>
                <OMA><OMS cd="arith1" name="times"/>
                  <OMA><OMS cd="arith1" name="unary_minus"/>
                    <OMI>3</OMI>
                  </OMA>
                  <OMS cd="nums1" name="i"/>
                  <OMA>
                    <OMS cd="arith1" name="divide"/>
                    <OMS cd="nums1" name="pi"/><OMI>4</OMI>
                  </OMA>
                </OMA>
              </OMA>
            </OMA>
          </OMA>
        </OMA>
      </OMA>
    </OMOBJ>

eq (minus (KelvinKer ( nu, x) , times (i, KelvinKei ( nu, x) ) ) , times (exp (times (unary_minus ( nu) , i, divide (pi, 2) ) ) , BesselK ( nu, times ( x, exp (times (unary_minus (3) , i, divide (pi, 4) ) ) ) ) ) )

Signatures:
sts


[Next: KelvinKei] [Previous: KelvinBei] [Top]

KelvinKei

KelvinKei This symbol takes two arguments, it represents a solution of the equations: KelvinKer(v,x) + I*KelvinKei(v,x) = exp(-v*Pi*I/2)*BesselK(v,x*exp(I*Pi/4)) and KelvinKer(v,x) - I*KelvinKei(v,x) = exp(-v*Pi*I/2)*BesselK(v,x*exp(-I*Pi/4))

Commented Mathematical property (CMP):
KelvinKer(v,x) + I*KelvinKei(v,x) = exp(-v*Pi*I/2)*BesselK(v,x*exp(I*Pi/4))
Formal Mathematical property (FMP):
<OMOBJ>
      <OMA><OMS cd="relation1" name="eq"/>
        <OMA><OMS cd="arith1" name="plus"/>
          <OMA><OMS cd="kelvin" name="KelvinKer"/>
            <OMV name="nu"/>
            <OMV name="x"/>
          </OMA>
          <OMA><OMS cd="arith1" name="times"/>
            <OMS cd="nums1" name="i"/>
            <OMA><OMS cd="kelvin" name="KelvinKei"/>
              <OMV name="nu"/>
              <OMV name="x"/>
            </OMA>
          </OMA>
        </OMA>
        <OMA><OMS cd="arith1" name="times"/>
          <OMA><OMS cd="transc1" name="exp"/>
            <OMA><OMS cd="arith1" name="times"/>
              <OMA><OMS cd="arith1" name="unary_minus"/>
                <OMV name="nu"/>
              </OMA>
              <OMS cd="nums1" name="i"/>
              <OMA><OMS cd="arith1" name="divide"/>
                <OMS cd="nums1" name="pi"/><OMI>2</OMI>
              </OMA>
            </OMA>
          </OMA>
          <OMA><OMS cd="bessel" name="BesselK"/>
            <OMV name="nu"/>
            <OMA><OMS cd="arith1" name="times"/>
              <OMV name="x"/>
              <OMA><OMS cd="transc1" name="exp"/>
                <OMA><OMS cd="arith1" name="times"/>
                  <OMI>3</OMI>
                  <OMS cd="nums1" name="i"/>
                  <OMA>
                    <OMS cd="arith1" name="divide"/>
                    <OMS cd="nums1" name="pi"/><OMI>4</OMI>
                  </OMA>
                </OMA>
              </OMA>
            </OMA>
          </OMA>
        </OMA>
      </OMA>
    </OMOBJ>

eq (plus (KelvinKer ( nu, x) , times (i, KelvinKei ( nu, x) ) ) , times (exp (times (unary_minus ( nu) , i, divide (pi, 2) ) ) , BesselK ( nu, times ( x, exp (times (3, i, divide (pi, 4) ) ) ) ) ) )

Commented Mathematical property (CMP):
KelvinKer(v,x) - I*KelvinKei(v,x) = exp(-v*Pi*I/2)*BesselK(v,x*exp(-I*Pi/4))
Formal Mathematical property (FMP):
<OMOBJ>
      <OMA><OMS cd="relation1" name="eq"/>
        <OMA><OMS cd="arith1" name="minus"/>
          <OMA><OMS cd="kelvin" name="KelvinKer"/>
            <OMV name="nu"/>
            <OMV name="x"/>
          </OMA>
          <OMA><OMS cd="arith1" name="times"/>
            <OMS cd="nums1" name="i"/>
            <OMA><OMS cd="kelvin" name="KelvinKei"/>
              <OMV name="nu"/>
              <OMV name="x"/>
            </OMA>
          </OMA>
        </OMA>
        <OMA><OMS cd="arith1" name="times"/>
          <OMA><OMS cd="transc1" name="exp"/>
            <OMA><OMS cd="arith1" name="times"/>
              <OMA><OMS cd="arith1" name="unary_minus"/>
                <OMV name="nu"/>
              </OMA>
              <OMS cd="nums1" name="i"/>
              <OMA><OMS cd="arith1" name="divide"/>
                <OMS cd="nums1" name="pi"/><OMI>2</OMI>
              </OMA>
            </OMA>
          </OMA>
          <OMA><OMS cd="bessel" name="BesselK"/>
            <OMV name="nu"/>
            <OMA><OMS cd="arith1" name="times"/>
              <OMV name="x"/>
              <OMA><OMS cd="transc1" name="exp"/>
                <OMA><OMS cd="arith1" name="times"/>
                  <OMA><OMS cd="arith1" name="unary_minus"/>
                    <OMI>3</OMI>
                  </OMA>
                  <OMS cd="nums1" name="i"/>
                  <OMA>
                    <OMS cd="arith1" name="divide"/>
                    <OMS cd="nums1" name="pi"/><OMI>4</OMI>
                  </OMA>
                </OMA>
              </OMA>
            </OMA>
          </OMA>
        </OMA>
      </OMA>
    </OMOBJ>

eq (minus (KelvinKer ( nu, x) , times (i, KelvinKei ( nu, x) ) ) , times (exp (times (unary_minus ( nu) , i, divide (pi, 2) ) ) , BesselK ( nu, times ( x, exp (times (unary_minus (3) , i, divide (pi, 4) ) ) ) ) ) )

Signatures:
sts


[Next: KelvinHer] [Previous: KelvinKer] [Top]

KelvinHer

KelvinHer This symbol takes two arguments, it represents a solution of the equations: KelvinHer(v,x) + I*KelvinHei(v,x) = HankelH1(v,x*exp(3*I*Pi/4)) and KelvinHer(v,x) - I*KelvinHei(v,x) = HankelH2(v,x*exp(-3*I*Pi/4))

Commented Mathematical property (CMP):
KelvinHer(v,x) + I*KelvinHei(v,x) = HankelH1(v,x*exp(3*I*Pi/4))
Formal Mathematical property (FMP):
<OMOBJ>
      <OMA><OMS cd="relation1" name="eq"/>
        <OMA><OMS cd="arith1" name="minus"/>
          <OMA><OMS cd="kelvin" name="KelvinHer"/>
            <OMV name="nu"/>
            <OMV name="x"/>
          </OMA>
          <OMA><OMS cd="arith1" name="times"/>
            <OMS cd="nums1" name="i"/>
            <OMA><OMS cd="kelvin" name="KelvinHei"/>
              <OMV name="nu"/>
              <OMV name="x"/>
            </OMA>
          </OMA>
        </OMA>
        <OMA><OMS cd="bessel" name="HankelH2"/>
          <OMV name="nu"/>
          <OMA><OMS cd="arith1" name="times"/>
            <OMV name="x"/>
            <OMA><OMS cd="transc1" name="exp"/>
              <OMA><OMS cd="arith1" name="times"/>
                <OMA><OMS cd="arith1" name="unary_minus"/>
                  <OMI>3</OMI>
                </OMA>
                <OMS cd="nums1" name="i"/>
                <OMA>
                  <OMS cd="arith1" name="divide"/>
                  <OMS cd="nums1" name="pi"/><OMI>4</OMI>
                </OMA>
              </OMA>
            </OMA>
          </OMA>
        </OMA>
      </OMA>
    </OMOBJ>

eq (minus (KelvinHer ( nu, x) , times (i, KelvinHei ( nu, x) ) ) , HankelH2 ( nu, times ( x, exp (times (unary_minus (3) , i, divide (pi, 4) ) ) ) ) )

Signatures:
sts


[Next: KelvinHei] [Previous: KelvinKei] [Top]
KelvinHer(v,x) - I*KelvinHei(v,x) = HankelH2(v,x*exp(-3*I*Pi/4))

KelvinHei

KelvinHei This symbol takes two arguments, it represents a solution of the equations: KelvinHer(v,x) + I*KelvinHei(v,x) = HankelH1(v,x*exp(3*I*Pi/4)) and KelvinHer(v,x) - I*KelvinHei(v,x) = HankelH2(v,x*exp(-3*I*Pi/4))

Commented Mathematical property (CMP):
KelvinHer(v,x) + I*KelvinHei(v,x) = HankelH1(v,x*exp(3*I*Pi/4))
Formal Mathematical property (FMP):
<OMOBJ>
      <OMA><OMS cd="relation1" name="eq"/>
        <OMA><OMS cd="arith1" name="plus"/>
          <OMA><OMS cd="kelvin" name="KelvinHer"/>
            <OMV name="nu"/>
            <OMV name="x"/>
          </OMA>
          <OMA><OMS cd="arith1" name="times"/>
            <OMS cd="nums1" name="i"/>
            <OMA><OMS cd="kelvin" name="KelvinHei"/>
              <OMV name="nu"/>
              <OMV name="x"/>
            </OMA>
          </OMA>
        </OMA>
        <OMA><OMS cd="bessel" name="HankelH1"/>
          <OMV name="nu"/>
          <OMA><OMS cd="arith1" name="times"/>
            <OMV name="x"/>
            <OMA><OMS cd="transc1" name="exp"/>
              <OMA><OMS cd="arith1" name="times"/>
                <OMI>3</OMI>
                <OMS cd="nums1" name="i"/>
                <OMA>
                  <OMS cd="arith1" name="divide"/>
                  <OMS cd="nums1" name="pi"/><OMI>4</OMI>
                </OMA>
              </OMA>
            </OMA>
          </OMA>
        </OMA>
      </OMA>
    </OMOBJ>

eq (plus (KelvinHer ( nu, x) , times (i, KelvinHei ( nu, x) ) ) , HankelH1 ( nu, times ( x, exp (times (3, i, divide (pi, 4) ) ) ) ) )

Commented Mathematical property (CMP):
KelvinHer(v,x) - I*KelvinHei(v,x) = HankelH2(v,x*exp(-3*I*Pi/4))
Formal Mathematical property (FMP):
<OMOBJ>
      <OMA><OMS cd="relation1" name="eq"/>
        <OMA><OMS cd="arith1" name="minus"/>
          <OMA><OMS cd="kelvin" name="KelvinHer"/>
            <OMV name="nu"/>
            <OMV name="x"/>
          </OMA>
          <OMA><OMS cd="arith1" name="times"/>
            <OMS cd="nums1" name="i"/>
            <OMA><OMS cd="kelvin" name="KelvinHei"/>
              <OMV name="nu"/>
              <OMV name="x"/>
            </OMA>
          </OMA>
        </OMA>
        <OMA><OMS cd="bessel" name="HankelH2"/>
          <OMV name="nu"/>
          <OMA><OMS cd="arith1" name="times"/>
            <OMV name="x"/>
            <OMA><OMS cd="transc1" name="exp"/>
              <OMA><OMS cd="arith1" name="times"/>
                <OMA><OMS cd="arith1" name="unary_minus"/>
                  <OMI>3</OMI>
                </OMA>
                <OMS cd="nums1" name="i"/>
                <OMA>
                  <OMS cd="arith1" name="divide"/>
                  <OMS cd="nums1" name="pi"/><OMI>4</OMI>
                </OMA>
              </OMA>
            </OMA>
          </OMA>
        </OMA>
      </OMA>
    </OMOBJ>

eq (minus (KelvinHer ( nu, x) , times (i, KelvinHei ( nu, x) ) ) , HankelH2 ( nu, times ( x, exp (times (unary_minus (3) , i, divide (pi, 4) ) ) ) ) )

Signatures:
sts


[First: KelvinBer] [Previous: KelvinHer] [Top]