http://www.mapleprimes.com/questions/142626-Special-Whittaker-Functions en-us 2026 Maplesoft, A Division of Waterloo Maple Inc. Maplesoft Document System Sat, 13 Jun 2026 21:00:40 GMT Sat, 13 Jun 2026 21:00:40 GMT The latest answers and comments added to the Question, special whittaker functions http://www.mapleprimes.com/images/mapleprimeswhite.jpg http://www.mapleprimes.com/questions/142626-Special-Whittaker-Functions http://www.mapleprimes.com/questions/142626-Special-Whittaker-Functions?ref=Feed:MaplePrimes:special whittaker functions:Comments#answer142632 <p>It can be done in such a way.</p> <p>&nbsp;</p> <form name="worksheet_form"> <table style="width: 576px;" align="center"> <tbody> <tr> <td> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><img style="vertical-align: -6;" src="/view.aspx?sf=142632/452304/0b06edccc13edc2b0b58533c85a21540.gif" alt="a := diff(u(t), `$`(t, 2))+(p^2-I+t^2)*u(t) = 0;" width="299" height="23"></p> <table> <tbody> <tr valign="baseline"> <td> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="center"><img style="vertical-align: -20;" src="/view.aspx?sf=142632/452304/41121fab7cf0a1bf6151f15c7520f6b5.gif" alt="diff(diff(u(t), t), t)+(p^2-I+t^2)*u(t) = 0" width="216" height="50"></p> </td> <td style="color: #000000; font-family: Times, serif; font-weight: bold; font-style: normal;" align="right">(1)</td> </tr> </tbody> </table> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><img style="vertical-align: -6;" src="/view.aspx?sf=142632/452304/256e2230cba6663591c8cf43a762765b.gif" alt="b := dsolve(a)" width="98" height="23"></p> <table> <tbody> <tr valign="baseline"> <td> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="center"><img style="vertical-align: -79;" src="/view.aspx?sf=142632/452304/c7b04570b7f96fc35d7e14649d006454.gif" alt="u(t) = _C1*WhittakerM(-1/4-((1/4)*I)*p^2, 1/4, I*t^2)/t^(1/2)+_C2*WhittakerW(-1/4-((1/4)*I)*p^2, 1/4, I*t^2)/t^(1/2)" width="546" height="124" align="middle"></p> </td> <td style="color: #000000; font-family: Times, serif; font-weight: bold; font-style: normal;" align="right">(2)</td> </tr> </tbody> </table> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><img style="vertical-align: -6;" src="/view.aspx?sf=142632/452304/215a0969cc3e1ea48a5346ee581f2d2e.gif" alt="convert(rhs(b), CylinderV)" width="174" height="23"></p> <table> <tbody> <tr valign="baseline"> <td> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="center"><img style="vertical-align: -269;" src="/view.aspx?sf=142632/452304/41097fa38fe5ac7f10d3f10fc4fe66de.gif" alt="(-1/2+(1/2)*I)*_C1*(CylinderV(1/2+((1/2)*I)*p^2, (-1-I)*t)-CylinderV(1/2+((1/2)*I)*p^2, (1+I)*t))*(I*t^2)^(3/4)*Pi*2^(((1/4)*I)*p^2)*(1+sin((1/2)*Pi*(1+I*p^2)))/(t^(3/2)*2^(1+((1/2)*I)*p^2)*cos((1/2)*Pi*(1+I*p^2))^2*GAMMA(1+((1/4)*I)*p^2))+_C2*Pi*(CylinderV(1/2+((1/2)*I)*p^2, -(I*t^2)^(1/2)*2^(1/2))-sin((1/2)*Pi*(1+I*p^2))*CylinderV(1/2+((1/2)*I)*p^2, (I*t^2)^(1/2)*2^(1/2)))*(I*t^2)^(1/4)*2^(1/2+((1/4)*I)*p^2)/(t^(1/2)*cos((1/2)*Pi*(1+I*p^2))^2*GAMMA(1+((1/2)*I)*p^2))" width="546" height="305" align="middle"></p> </td> <td style="color: #000000; font-family: Times, serif; font-weight: bold; font-style: normal;" align="right">(3)</td> </tr> </tbody> </table> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><img style="vertical-align: -6;" src="/view.aspx?sf=142632/452304/1419cb804d96f50b87be6ef901bf2fd7.gif" alt="``" width="11" height="23"></p> </td> </tr> </tbody> </table> <input type="hidden" name="sequence" value="1"> <input type="hidden" name="cmd" value="none"></form> <p>&nbsp;</p> <p><a href="/view.aspx?sf=142632/452304/CylinderV.mw">Download CylinderV.mw</a></p> <form name="worksheet_form"><input type="hidden" name="sequence" value="1"> <input type="hidden" name="cmd" value="none"></form> <p>&nbsp;</p> <p>&nbsp;</p> <p>See <a href="http://www.maplesoft.com/support/help/search.aspx?term=convert,Cylinder">?convert,Cylinder</a> and <a href="http://www.maplesoft.com/support/help/search.aspx?term=Cylinder">?Cylinder</a> for more info.</p> <p>PS. <a href="/view.aspx?sf=142632/452307/screen25.01.13.docx">screen25.01.13.docx</a></p> <p>It can be done in such a way.</p> <p>&nbsp;</p> <form name="worksheet_form"> <table style="width: 576px;" align="center"> <tbody> <tr> <td> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><img style="vertical-align: -6;" src="/view.aspx?sf=142632/452304/0b06edccc13edc2b0b58533c85a21540.gif" alt="a := diff(u(t), `$`(t, 2))+(p^2-I+t^2)*u(t) = 0;" width="299" height="23"></p> <table> <tbody> <tr valign="baseline"> <td> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="center"><img style="vertical-align: -20;" src="/view.aspx?sf=142632/452304/41121fab7cf0a1bf6151f15c7520f6b5.gif" alt="diff(diff(u(t), t), t)+(p^2-I+t^2)*u(t) = 0" width="216" height="50"></p> </td> <td style="color: #000000; font-family: Times, serif; font-weight: bold; font-style: normal;" align="right">(1)</td> </tr> </tbody> </table> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><img style="vertical-align: -6;" src="/view.aspx?sf=142632/452304/256e2230cba6663591c8cf43a762765b.gif" alt="b := dsolve(a)" width="98" height="23"></p> <table> <tbody> <tr valign="baseline"> <td> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="center"><img style="vertical-align: -79;" src="/view.aspx?sf=142632/452304/c7b04570b7f96fc35d7e14649d006454.gif" alt="u(t) = _C1*WhittakerM(-1/4-((1/4)*I)*p^2, 1/4, I*t^2)/t^(1/2)+_C2*WhittakerW(-1/4-((1/4)*I)*p^2, 1/4, I*t^2)/t^(1/2)" width="546" height="124" align="middle"></p> </td> <td style="color: #000000; font-family: Times, serif; font-weight: bold; font-style: normal;" align="right">(2)</td> </tr> </tbody> </table> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><img style="vertical-align: -6;" src="/view.aspx?sf=142632/452304/215a0969cc3e1ea48a5346ee581f2d2e.gif" alt="convert(rhs(b), CylinderV)" width="174" height="23"></p> <table> <tbody> <tr valign="baseline"> <td> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="center"><img style="vertical-align: -269;" src="/view.aspx?sf=142632/452304/41097fa38fe5ac7f10d3f10fc4fe66de.gif" alt="(-1/2+(1/2)*I)*_C1*(CylinderV(1/2+((1/2)*I)*p^2, (-1-I)*t)-CylinderV(1/2+((1/2)*I)*p^2, (1+I)*t))*(I*t^2)^(3/4)*Pi*2^(((1/4)*I)*p^2)*(1+sin((1/2)*Pi*(1+I*p^2)))/(t^(3/2)*2^(1+((1/2)*I)*p^2)*cos((1/2)*Pi*(1+I*p^2))^2*GAMMA(1+((1/4)*I)*p^2))+_C2*Pi*(CylinderV(1/2+((1/2)*I)*p^2, -(I*t^2)^(1/2)*2^(1/2))-sin((1/2)*Pi*(1+I*p^2))*CylinderV(1/2+((1/2)*I)*p^2, (I*t^2)^(1/2)*2^(1/2)))*(I*t^2)^(1/4)*2^(1/2+((1/4)*I)*p^2)/(t^(1/2)*cos((1/2)*Pi*(1+I*p^2))^2*GAMMA(1+((1/2)*I)*p^2))" width="546" height="305" align="middle"></p> </td> <td style="color: #000000; font-family: Times, serif; font-weight: bold; font-style: normal;" align="right">(3)</td> </tr> </tbody> </table> <p style="margin: 0 0 0 0; padding-top: 0px; padding-bottom: 0px;" align="left"><img style="vertical-align: -6;" src="/view.aspx?sf=142632/452304/1419cb804d96f50b87be6ef901bf2fd7.gif" alt="``" width="11" height="23"></p> </td> </tr> </tbody> </table> <input type="hidden" name="sequence" value="1"> <input type="hidden" name="cmd" value="none"></form> <p>&nbsp;</p> <p><a href="/view.aspx?sf=142632/452304/CylinderV.mw">Download CylinderV.mw</a></p> <form name="worksheet_form"><input type="hidden" name="sequence" value="1"> <input type="hidden" name="cmd" value="none"></form> <p>&nbsp;</p> <p>&nbsp;</p> <p>See <a href="http://www.maplesoft.com/support/help/search.aspx?term=convert,Cylinder">?convert,Cylinder</a> and <a href="http://www.maplesoft.com/support/help/search.aspx?term=Cylinder">?Cylinder</a> for more info.</p> <p>PS. <a href="/view.aspx?sf=142632/452307/screen25.01.13.docx">screen25.01.13.docx</a></p> 142632 Sat, 26 Jan 2013 01:51:06 Z Markiyan Hirnyk Markiyan Hirnyk http://www.mapleprimes.com/questions/142626-Special-Whittaker-Functions?ref=Feed:MaplePrimes:special whittaker functions:Comments#comment142644 <p>Thanks, this has been helpful</p> <p>Thanks, this has been helpful</p> 142644 Sat, 26 Jan 2013 17:39:47 Z gdog gdog