uu.seUppsala University Publications

CiteExport$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_upper_j_idt155",{id:"formSmash:upper:j_idt155",widgetVar:"widget_formSmash_upper_j_idt155",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:upper:exportLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_upper_j_idt156_j_idt164",{id:"formSmash:upper:j_idt156:j_idt164",widgetVar:"widget_formSmash_upper_j_idt156_j_idt164",target:"formSmash:upper:j_idt156:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});

A new method *q*-calculusPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
function selectAll()
{
var panelSome = $(PrimeFaces.escapeClientId("formSmash:some"));
var panelAll = $(PrimeFaces.escapeClientId("formSmash:all"));
panelAll.toggle();
toggleList(panelSome.get(0).childNodes, panelAll);
toggleList(panelAll.get(0).childNodes, panelAll);
}
/*Toggling the list of authorPanel nodes according to the toggling of the closeable second panel */
function toggleList(childList, panel)
{
var panelWasOpen = (panel.get(0).style.display == 'none');
// console.log('panel was open ' + panelWasOpen);
for (var c = 0; c < childList.length; c++) {
if (childList[c].classList.contains('authorPanel')) {
clickNode(panelWasOpen, childList[c]);
}
}
}
/*nodes have styleClass ui-corner-top if they are expanded and ui-corner-all if they are collapsed */
function clickNode(collapse, child)
{
if (collapse && child.classList.contains('ui-corner-top')) {
// console.log('collapse');
child.click();
}
if (!collapse && child.classList.contains('ui-corner-all')) {
// console.log('expand');
child.click();
}
}
2002 (English)Doctoral thesis, monograph (Other academic)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Uppsala: Acta Universitatis Upsaliensis , 2002. , p. 116
##### Series

Uppsala Dissertations in Mathematics, ISSN 1401-2049 ; 25
##### Keywords [en]

Mathematics
##### Keywords [sv]

MATEMATIK
##### National Category

Mathematics
##### Research subject

Mathematics
##### Identifiers

URN: urn:nbn:se:uu:diva-2698ISBN: 91-506-1628-5 (print)OAI: oai:DiVA.org:uu-2698DiVA, id: diva2:162070
##### Public defence

2002-11-14, Room 2146, Mathematics and Information Technology Center, Polacksbacken, Uppsala, 13:15
##### Opponent

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt508",{id:"formSmash:j_idt508",widgetVar:"widget_formSmash_j_idt508",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt514",{id:"formSmash:j_idt514",widgetVar:"widget_formSmash_j_idt514",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt520",{id:"formSmash:j_idt520",widgetVar:"widget_formSmash_j_idt520",multiple:true}); Available from: 2002-10-17 Created: 2002-10-17Bibliographically approved

In *q-*calculus we are looking for *q-*analogues of mathematical objects, which have the original object as limits when *q* tends to 1. *q*-Calculus has wide-ranging applications in analytic number theory and theoretical physics. The main topic of the thesis is the invention of the tilde operator and the renaissance of the *q-*addition. There are two types of *q-*addition, the Ward-AlSalam *q-*addition and the Hahn *q-*addition. The first is both commutative and associative, while the second is neither. This is one of the reasons why sometimes more than one *q-*analogue exist. These two operators form the basis of the method which unites hypergeometric series and *q-*hypergeometric series and which gives many formulas of *q-*calculus a natural form reminding directly of their classical origin. This method is reminiscent of Heine, who mentioned the case where one parameter in a *q-*hypergeometric series is plus infinity. The *q-*addition is the natural way to extend addition to the *q-*case as is shown when restating addition formulas for *q-*trigonometric functions.

We give a more lucid definition of the *q-*difference operator. A new notation for powers of *q* reminding of the exponential function is given. A *q-*Taylor formula with remainder term expressed as *q-*integral is proved.

We present a new expression for generalized Vandermonde determinants, and thus for the Schur function. We also obtain an equivalence relation on the set of all generalized Vandermonde determinants. We find a more general expression for the Vandermonde determinant. We show the connection to a determinant of Flowe and Harris and to the solution of difference and *q-*difference equations with constant coefficients.

isbn
urn-nbn$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_j_idt1520",{id:"formSmash:j_idt1520",widgetVar:"widget_formSmash_j_idt1520",showEffect:"fade",hideEffect:"fade",showDelay:500,hideDelay:300,target:"formSmash:altmetricDiv"});});

CiteExport$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_lower_j_idt1573",{id:"formSmash:lower:j_idt1573",widgetVar:"widget_formSmash_lower_j_idt1573",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:lower:exportLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_lower_j_idt1574_j_idt1576",{id:"formSmash:lower:j_idt1574:j_idt1576",widgetVar:"widget_formSmash_lower_j_idt1574_j_idt1576",target:"formSmash:lower:j_idt1574:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});