Ratio of Gamma function equality. The 2019 Stack Overflow Developer Survey Results Are InIncomplete gamma functionPartial Fractions Decomposition of the Gamma FunctionProof of a formula involving Gamma functionUpper bound on ratio of incomplete Gamma function and Gamma function $frac Gamma left( x; aright)Gamma(x)$What substitution (to be used in integration) can proof the following equality?Power series of a function related to Gamma functionQusetion about Gamma functionEquality of Ratio of Gamma FunctionsGamma fuction of odd numbers divided by 2Asymptotic approximation regarding the Gamma function $Gamma$.

Inverse Relationship Between Precision and Recall

What is the motivation for a law requiring 2 parties to consent for recording a conversation

What do I do when my TA workload is more than expected?

How to type a long/em dash `—`

Pokemon Turn Based battle (Python)

Can withdrawing asylum be illegal?

Star Trek - X-shaped Item on Regula/Orbital Office Starbases

Is it safe to harvest rainwater that fell on solar panels?

How to charge AirPods to keep battery healthy?

What does Linus Torvalds mean when he says that Git "never ever" tracks a file?

Why didn't the Event Horizon Telescope team mention Sagittarius A*?

What do these terms in Caesar's Gallic wars mean?

If I score a critical hit on an 18 or higher, what are my chances of getting a critical hit if I roll 3d20?

Currents/voltages graph for an electrical circuit

Why doesn't UInt have a toDouble()?

Is it okay to consider publishing in my first year of PhD?

How to support a colleague who finds meetings extremely tiring?

Keeping a retro style to sci-fi spaceships?

Output the Arecibo Message

The phrase "to the numbers born"?

Dropping list elements from nested list after evaluation

Is an up-to-date browser secure on an out-of-date OS?

Straighten subgroup lattice

What is the most efficient way to store a numeric range?



Ratio of Gamma function equality.



The 2019 Stack Overflow Developer Survey Results Are InIncomplete gamma functionPartial Fractions Decomposition of the Gamma FunctionProof of a formula involving Gamma functionUpper bound on ratio of incomplete Gamma function and Gamma function $frac Gamma left( x; aright)Gamma(x)$What substitution (to be used in integration) can proof the following equality?Power series of a function related to Gamma functionQusetion about Gamma functionEquality of Ratio of Gamma FunctionsGamma fuction of odd numbers divided by 2Asymptotic approximation regarding the Gamma function $Gamma$.










0












$begingroup$


Let $m,ninmathbb N$ with $m<n$ and $0<s<1$, $1leq p<infty$. Is the following holds $$fracGamma(fracsp+p+n-22)Gamma(fracn-m+sp2)Gamma(fracn+sp2)Gamma(fracsp+p+n-m-22)=1.$$
Where $Gamma$ is the usual gamma function.



Clearly for $p=2$, its true.



I'm trying to show this for any $p$ with the above range but couldn't do.






real-analysis integration complex-analysis gamma-function







share|cite|improve this question









$endgroup$
















    0












    $begingroup$


    Let $m,ninmathbb N$ with $m<n$ and $0<s<1$, $1leq p<infty$. Is the following holds $$fracGamma(fracsp+p+n-22)Gamma(fracn-m+sp2)Gamma(fracn+sp2)Gamma(fracsp+p+n-m-22)=1.$$
    Where $Gamma$ is the usual gamma function.



    Clearly for $p=2$, its true.



    I'm trying to show this for any $p$ with the above range but couldn't do.






    real-analysis integration complex-analysis gamma-function







    share|cite|improve this question









    $endgroup$














      0












      0








      0





      $begingroup$


      Let $m,ninmathbb N$ with $m<n$ and $0<s<1$, $1leq p<infty$. Is the following holds $$fracGamma(fracsp+p+n-22)Gamma(fracn-m+sp2)Gamma(fracn+sp2)Gamma(fracsp+p+n-m-22)=1.$$
      Where $Gamma$ is the usual gamma function.



      Clearly for $p=2$, its true.



      I'm trying to show this for any $p$ with the above range but couldn't do.






      real-analysis integration complex-analysis gamma-function







      share|cite|improve this question









      $endgroup$




      Let $m,ninmathbb N$ with $m<n$ and $0<s<1$, $1leq p<infty$. Is the following holds $$fracGamma(fracsp+p+n-22)Gamma(fracn-m+sp2)Gamma(fracn+sp2)Gamma(fracsp+p+n-m-22)=1.$$
      Where $Gamma$ is the usual gamma function.



      Clearly for $p=2$, its true.



      I'm trying to show this for any $p$ with the above range but couldn't do.






      real-analysis integration complex-analysis gamma-function




      real-analysis integration complex-analysis gamma-function






      share|cite|improve this question













      share|cite|improve this question











      share|cite|improve this question




      share|cite|improve this question










      asked Mar 30 at 21:16









      MathRockMathRock

      316




      316




















          1 Answer
          1






          active

          oldest

          votes


















          1












          $begingroup$

          For example with $m=1$ , $n=2$ , $s=frac12$ , $p=4$



          $Gamma(fracsp+p+n-22)= 2$



          $Gamma(fracn-m+sp2) = fracsqrtpi2$



          $Gamma(fracn+sp2) = 1$



          $Gamma(fracsp+p+n-m-22) = frac3sqrtpi4$



          $$fracGamma(fracsp+p+n-22) Gamma(fracn-m+sp2) Gamma(fracn+sp2) Gamma(fracsp+p+n-m-22) = frac2fracsqrtpi21frac3sqrtpi4 = frac43$$



          The result is different from $1$.



          Thus, $fracGamma(fracsp+p+n-22) Gamma(fracn-m+sp2) Gamma(fracn+sp2) Gamma(fracsp+p+n-m-22) $ is not always equal to $1$.






          share|cite|improve this answer









          $endgroup$













            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',
            autoActivateHeartbeat: false,
            convertImagesToLinks: true,
            noModals: true,
            showLowRepImageUploadWarning: true,
            reputationToPostImages: 10,
            bindNavPrevention: true,
            postfix: "",
            imageUploader:
            brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
            contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
            allowUrls: true
            ,
            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%2f3168788%2fratio-of-gamma-function-equality%23new-answer', 'question_page');

            );

            Post as a guest















            Required, but never shown

























            1 Answer
            1






            active

            oldest

            votes








            1 Answer
            1






            active

            oldest

            votes









            active

            oldest

            votes






            active

            oldest

            votes









            1












            $begingroup$

            For example with $m=1$ , $n=2$ , $s=frac12$ , $p=4$



            $Gamma(fracsp+p+n-22)= 2$



            $Gamma(fracn-m+sp2) = fracsqrtpi2$



            $Gamma(fracn+sp2) = 1$



            $Gamma(fracsp+p+n-m-22) = frac3sqrtpi4$



            $$fracGamma(fracsp+p+n-22) Gamma(fracn-m+sp2) Gamma(fracn+sp2) Gamma(fracsp+p+n-m-22) = frac2fracsqrtpi21frac3sqrtpi4 = frac43$$



            The result is different from $1$.



            Thus, $fracGamma(fracsp+p+n-22) Gamma(fracn-m+sp2) Gamma(fracn+sp2) Gamma(fracsp+p+n-m-22) $ is not always equal to $1$.






            share|cite|improve this answer









            $endgroup$

















              1












              $begingroup$

              For example with $m=1$ , $n=2$ , $s=frac12$ , $p=4$



              $Gamma(fracsp+p+n-22)= 2$



              $Gamma(fracn-m+sp2) = fracsqrtpi2$



              $Gamma(fracn+sp2) = 1$



              $Gamma(fracsp+p+n-m-22) = frac3sqrtpi4$



              $$fracGamma(fracsp+p+n-22) Gamma(fracn-m+sp2) Gamma(fracn+sp2) Gamma(fracsp+p+n-m-22) = frac2fracsqrtpi21frac3sqrtpi4 = frac43$$



              The result is different from $1$.



              Thus, $fracGamma(fracsp+p+n-22) Gamma(fracn-m+sp2) Gamma(fracn+sp2) Gamma(fracsp+p+n-m-22) $ is not always equal to $1$.






              share|cite|improve this answer









              $endgroup$















                1












                1








                1





                $begingroup$

                For example with $m=1$ , $n=2$ , $s=frac12$ , $p=4$



                $Gamma(fracsp+p+n-22)= 2$



                $Gamma(fracn-m+sp2) = fracsqrtpi2$



                $Gamma(fracn+sp2) = 1$



                $Gamma(fracsp+p+n-m-22) = frac3sqrtpi4$



                $$fracGamma(fracsp+p+n-22) Gamma(fracn-m+sp2) Gamma(fracn+sp2) Gamma(fracsp+p+n-m-22) = frac2fracsqrtpi21frac3sqrtpi4 = frac43$$



                The result is different from $1$.



                Thus, $fracGamma(fracsp+p+n-22) Gamma(fracn-m+sp2) Gamma(fracn+sp2) Gamma(fracsp+p+n-m-22) $ is not always equal to $1$.






                share|cite|improve this answer









                $endgroup$



                For example with $m=1$ , $n=2$ , $s=frac12$ , $p=4$



                $Gamma(fracsp+p+n-22)= 2$



                $Gamma(fracn-m+sp2) = fracsqrtpi2$



                $Gamma(fracn+sp2) = 1$



                $Gamma(fracsp+p+n-m-22) = frac3sqrtpi4$



                $$fracGamma(fracsp+p+n-22) Gamma(fracn-m+sp2) Gamma(fracn+sp2) Gamma(fracsp+p+n-m-22) = frac2fracsqrtpi21frac3sqrtpi4 = frac43$$



                The result is different from $1$.



                Thus, $fracGamma(fracsp+p+n-22) Gamma(fracn-m+sp2) Gamma(fracn+sp2) Gamma(fracsp+p+n-m-22) $ is not always equal to $1$.







                share|cite|improve this answer












                share|cite|improve this answer



                share|cite|improve this answer










                answered Mar 30 at 22:14









                JJacquelinJJacquelin

                45.6k21857




                45.6k21857



























                    draft saved

                    draft discarded
















































                    Thanks for contributing an answer to Mathematics Stack Exchange!


                    • Please be sure to answer the question. Provide details and share your research!

                    But avoid …


                    • Asking for help, clarification, or responding to other answers.

                    • Making statements based on opinion; back them up with references or personal experience.

                    Use MathJax to format equations. MathJax reference.


                    To learn more, see our tips on writing great answers.




                    draft saved


                    draft discarded














                    StackExchange.ready(
                    function ()
                    StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3168788%2fratio-of-gamma-function-equality%23new-answer', 'question_page');

                    );

                    Post as a guest















                    Required, but never shown





















































                    Required, but never shown














                    Required, but never shown












                    Required, but never shown







                    Required, but never shown

































                    Required, but never shown














                    Required, but never shown












                    Required, but never shown







                    Required, but never shown







                    -

                    Popular posts from this blog

                    Boston (Lincolnshire) Stedsbyld | Berne yn Boston | NavigaasjemenuBoston Borough CouncilBoston, Lincolnshire

                    Image
                    HânzestêdPlak yn Lincolnshire bestjoerlike gebietBostonIngelskegreefskipLincolnshireWithamThe WashThe Fens1545Boston Boston (Lincolnshire) Ut Wikipedy Jump to navigation Jump to search Boston De Boston Stump Sifers Ynwennertal 35.124 (2001) Befolkingstichtens 1244 km² Polityk Lân Feriene Keninkryk Regio East Midlands Greefskip Lincolnshire Oar Tiidsône GMT Simmertiid (UTC+1) Webside Boston Borough Council Lizzing fan Boston yn Ingelân Boston is in lytse âlde havenstêd ( town ) yn it bestjoerlike gebiet Boston, yn it Ingelske greefskip Lincolnshire. It plak hie 35.124 ynwenners yn 2001. De stêd leit oan de rivier de Witham, sa'n seis kilometer fan it plak dêr't de Witham yn it estuarium The Wash streamt. It plak leit yn it flakke, sompige en agrarysk gebiet The Fens. Boston syn meast opfallende gebou is de St Botolph's-tsjerke ( The Stump ), boud fan 1309 oant 1460; it is de grutste parish -tsjerke...
                    Read more

                    Trouble understanding the speech of overseas colleaguesHow can I better understand manager or clients with strong accents?Adding more movement and speech at the fundamental level to a highly-sedentary job?Difficulty in understanding Manager's accent(language and communication)How to adjust yourself where your colleagues are not understanding to you?Understanding manager's expectationsForeigner and colleagues using slangHaving difficulty understanding meetingsHow do you breathe when giving a speech?Trouble Waking Up for Emergencies (On-Call)Problems with colleaguesColleagues feeling insecure when I do my work

                    Image
                    Number of words that can be made using all the letters of the word W, if Os as well as Is are separated is? Class Action - which options I have? Do the temporary hit points from the Battlerager barbarian's Reckless Abandon stack if I make multiple attacks on my turn? Implement the Thanos sorting algorithm Invade the Pyramid if you Dare Lay out the Carpet How can I get through very long and very dry, but also very useful technical documents when learning a new tool? A Rare Riley Riddle Why Were Madagascar and New Zealand Discovered So Late? How do I extract a value from a time formatted value in excel? Inappropriate reference requests from Journal reviewers How can I quit an app using Terminal? How do we know the LHC results are robust? Escape a mm/dd/YY backup date in a file name Why escape if the_content isnt? Do sorcerers' Subtle Spells require a skill check to be unseen? Sort a list by elements of another list What does 算不上 mean ...
                    Read more

                    Is the concept of a “numerable” fiber bundle really useful or an empty generalization?Non trivial vector bundle over non-paracompact contractible spaceExample of fiber bundle that is not a fibrationGlobalising fibrations by schedulesFiber bundle = principal bundle + fiber?Numerable covers from the point of view of Grothendieck topologiesGlobal sections for torus fiber bundleAre there analogs of smooth partitions of unity and good open covers for PL-manifolds?Two natural maps asssociated with the nerve of a coverDescent theory, fibrations, and bundlesIn which sense are Euler-Lagrange PDE's on fiber bundles quasi-linear?What is the local structure of a fibration?Complete proof of Homotopy invariance of a numerable fiber bundle based on CHPLocally trivial fibration over a suspension

                    Image
                    Is the concept of a “numerable” fiber bundle really useful or an empty generalization? Non trivial vector bundle over non-paracompact contractible spaceExample of fiber bundle that is not a fibrationGlobalising fibrations by schedulesFiber bundle = principal bundle + fiber?Numerable covers from the point of view of Grothendieck topologiesGlobal sections for torus fiber bundleAre there analogs of smooth partitions of unity and good open covers for PL-manifolds?Two natural maps asssociated with the nerve of a coverDescent theory, fibrations, and bundlesIn which sense are Euler-Lagrange PDE's on fiber bundles quasi-linear?What is the local structure of a fibration?Complete proof of Homotopy invariance of a numerable fiber bundle based on CHPLocally trivial fibration over a suspension 13 4 $begingroup$ Numerable fiber bundles are defined by Dold (DOLD 1962 - Partitions of Unity in theory of Fibrations) as a generalization of fiber bundles over a paracompact space...
                    Read more