How do you solve $int_0^-inftyJ_0(br)e^iasqrtf_0^2-r^2rdr$

Multi tool use
Multi tool use

The name of the pictureThe name of the pictureThe name of the pictureClash Royale CLAN TAG#URR8PPP











up vote
0
down vote

favorite












How is solved this integral of Bessel function ?
$$int_0^-inftyJ_0(br)e^iasqrtf_0^2-r^2rdr$$



where $a, b$ are real numbers, $f_0>r$










share|cite|improve this question























  • Looks like a Hankel Transform. Maybe the corresponding 2D Fourier-Transform is easier ... ? Otherwise you may expand the Bessel Function in a power-series and then integrate. Also make sure to check out common intagral-tables, e.g. Gradshteyn Ryzhick. Finally: is $e^i a sqrtf_0^2-r^2 in L^1(]0,infty[)$?
    – denklo
    Sep 7 at 10:06














up vote
0
down vote

favorite












How is solved this integral of Bessel function ?
$$int_0^-inftyJ_0(br)e^iasqrtf_0^2-r^2rdr$$



where $a, b$ are real numbers, $f_0>r$










share|cite|improve this question























  • Looks like a Hankel Transform. Maybe the corresponding 2D Fourier-Transform is easier ... ? Otherwise you may expand the Bessel Function in a power-series and then integrate. Also make sure to check out common intagral-tables, e.g. Gradshteyn Ryzhick. Finally: is $e^i a sqrtf_0^2-r^2 in L^1(]0,infty[)$?
    – denklo
    Sep 7 at 10:06












up vote
0
down vote

favorite









up vote
0
down vote

favorite











How is solved this integral of Bessel function ?
$$int_0^-inftyJ_0(br)e^iasqrtf_0^2-r^2rdr$$



where $a, b$ are real numbers, $f_0>r$










share|cite|improve this question















How is solved this integral of Bessel function ?
$$int_0^-inftyJ_0(br)e^iasqrtf_0^2-r^2rdr$$



where $a, b$ are real numbers, $f_0>r$







integration transformation






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Sep 7 at 9:57









Bernard

112k635104




112k635104










asked Sep 7 at 9:47









ole

153




153











  • Looks like a Hankel Transform. Maybe the corresponding 2D Fourier-Transform is easier ... ? Otherwise you may expand the Bessel Function in a power-series and then integrate. Also make sure to check out common intagral-tables, e.g. Gradshteyn Ryzhick. Finally: is $e^i a sqrtf_0^2-r^2 in L^1(]0,infty[)$?
    – denklo
    Sep 7 at 10:06
















  • Looks like a Hankel Transform. Maybe the corresponding 2D Fourier-Transform is easier ... ? Otherwise you may expand the Bessel Function in a power-series and then integrate. Also make sure to check out common intagral-tables, e.g. Gradshteyn Ryzhick. Finally: is $e^i a sqrtf_0^2-r^2 in L^1(]0,infty[)$?
    – denklo
    Sep 7 at 10:06















Looks like a Hankel Transform. Maybe the corresponding 2D Fourier-Transform is easier ... ? Otherwise you may expand the Bessel Function in a power-series and then integrate. Also make sure to check out common intagral-tables, e.g. Gradshteyn Ryzhick. Finally: is $e^i a sqrtf_0^2-r^2 in L^1(]0,infty[)$?
– denklo
Sep 7 at 10:06




Looks like a Hankel Transform. Maybe the corresponding 2D Fourier-Transform is easier ... ? Otherwise you may expand the Bessel Function in a power-series and then integrate. Also make sure to check out common intagral-tables, e.g. Gradshteyn Ryzhick. Finally: is $e^i a sqrtf_0^2-r^2 in L^1(]0,infty[)$?
– denklo
Sep 7 at 10:06















active

oldest

votes











Your Answer




StackExchange.ifUsing("editor", function ()
return StackExchange.using("mathjaxEditing", function ()
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix)
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
);
);
, "mathjax-editing");

StackExchange.ready(function()
var channelOptions =
tags: "".split(" "),
id: "69"
;
initTagRenderer("".split(" "), "".split(" "), channelOptions);

StackExchange.using("externalEditor", function()
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled)
StackExchange.using("snippets", function()
createEditor();
);

else
createEditor();

);

function createEditor()
StackExchange.prepareEditor(
heartbeatType: 'answer',
convertImagesToLinks: true,
noModals: false,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
);



);













 

draft saved


draft discarded


















StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2908457%2fhow-do-you-solve-int-0-inftyj-0breia-sqrtf-02-r2rdr%23new-answer', 'question_page');

);

Post as a guest



































active

oldest

votes













active

oldest

votes









active

oldest

votes






active

oldest

votes















 

draft saved


draft discarded















































 


draft saved


draft discarded














StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2908457%2fhow-do-you-solve-int-0-inftyj-0breia-sqrtf-02-r2rdr%23new-answer', 'question_page');

);

Post as a guest













































































hD358,Kx,lq7ypS2E2U,5EiC,2xuBexenOxmcjOduUGr Oz7hhsg,n0MVi 9FMMHEAzXGPaxh Ia VuKBRgxvn7TJ
f,abngVxzxvvV,wNiU,oicY,r4tcF1wqd7 Xy5i9U,lLn vyfg l5j,uuKcEE84P 3,M

這個網誌中的熱門文章

How to combine Bézier curves to a surface?

Propositional logic and tautologies

Distribution of Stopped Wiener Process with Stochastic Volatility