A new rule in hyperexpand to get nice results for the Laplace transform of Fresnel functions
A new rule in hyperexpand to get nice results for the Laplace transform of Fresnel functions

Examples without this formula:

  laplace_transform(fresnels(t), t, s, noconds=True)

   ⎛         ⎛         │    4 ⎞        ⎛  2⎞        ⎛  2⎞⎞
   ⎜     ┌─  ⎜   1     │  -s  ⎟        ⎜ s ⎟        ⎜ s ⎟⎟
  -⎜2⋅s⋅ ├─  ⎜         │ ─────⎟ - π⋅sin⎜───⎟ - π⋅cos⎜───⎟⎟
   ⎜    1╵ 2 ⎜3/4, 5/4 │     2⎟        ⎝2⋅π⎠        ⎝2⋅π⎠⎟
   ⎝         ⎝         │ 16⋅π ⎠                          ⎠
  ────────────────────────────────────────────────────────
                           2⋅π⋅s

  laplace_transform(fresnelc(t), t, s, noconds=True)

            ⎛         │    4 ⎞           ⎛  2⎞           ⎛  2⎞
     3  ┌─  ⎜   1     │  -s  ⎟      2    ⎜ s ⎟      2    ⎜ s ⎟
  2⋅s ⋅ ├─  ⎜         │ ─────⎟ - 3⋅π ⋅sin⎜───⎟ + 3⋅π ⋅cos⎜───⎟
       1╵ 2 ⎜5/4, 7/4 │     2⎟           ⎝2⋅π⎠           ⎝2⋅π⎠
            ⎝         │ 16⋅π ⎠
  ────────────────────────────────────────────────────────────
                                2
                             6⋅π ⋅s

And with this formula we can expand the 1F2 above:

  laplace_transform(fresnels(t), t, s, noconds=True)

       ⎛  2⎞                  ⎛  2⎞      ⎛  2⎞                  ⎛  2⎞
       ⎜ s ⎟         ⎛s⎞      ⎜ s ⎟      ⎜ s ⎟         ⎛s⎞      ⎜ s ⎟
    sin⎜───⎟⋅fresnels⎜─⎟   sin⎜───⎟   cos⎜───⎟⋅fresnelc⎜─⎟   cos⎜───⎟
       ⎝2⋅π⎠         ⎝π⎠      ⎝2⋅π⎠      ⎝2⋅π⎠         ⎝π⎠      ⎝2⋅π⎠
  - ──────────────────── + ──────── - ──────────────────── + ────────
             s               2⋅s               s               2⋅s

  laplace_transform(fresnelc(t), t, s, noconds=True)

     ⎛  2⎞                  ⎛  2⎞      ⎛  2⎞                  ⎛  2⎞
     ⎜ s ⎟         ⎛s⎞      ⎜ s ⎟      ⎜ s ⎟         ⎛s⎞      ⎜ s ⎟
  sin⎜───⎟⋅fresnelc⎜─⎟   sin⎜───⎟   cos⎜───⎟⋅fresnels⎜─⎟   cos⎜───⎟
     ⎝2⋅π⎠         ⎝π⎠      ⎝2⋅π⎠      ⎝2⋅π⎠         ⎝π⎠      ⎝2⋅π⎠
  ──────────────────── - ──────── - ──────────────────── + ────────
           s               2⋅s               s               2⋅s

This result is nice and correct.

mcdaniel67/sympy,meghana1995/sympy,jaimahajan1997/sympy,MridulS/sympy,kmacinnis/sympy,debugger22/sympy,VaibhavAgarwalVA/sympy,abloomston/sympy,lindsayad/sympy,shipci/sympy,oliverlee/sympy,Designist/sympy,kevalds51/sympy,lindsayad/sympy,sahmed95/sympy,oliverlee/sympy,liangjiaxing/sympy,sahilshekhawat/sympy,beni55/sympy,moble/sympy,Arafatk/sympy,sunny94/temp,jerli/sympy,lidavidm/sympy,emon10005/sympy,yashsharan/sympy,jbbskinny/sympy,jbbskinny/sympy,amitjamadagni/sympy,kaichogami/sympy,abhiii5459/sympy,postvakje/sympy,Sumith1896/sympy,toolforger/sympy,postvakje/sympy,atsao72/sympy,yukoba/sympy,grevutiu-gabriel/sympy,jerli/sympy,vipulroxx/sympy,farhaanbukhsh/sympy,chaffra/sympy,madan96/sympy,pbrady/sympy,garvitr/sympy,Vishluck/sympy,ChristinaZografou/sympy,Gadal/sympy,wyom/sympy,mcdaniel67/sympy,hrashk/sympy,kaichogami/sympy,wyom/sympy,shikil/sympy,aktech/sympy,sahilshekhawat/sympy,maniteja123/sympy,Designist/sympy,Gadal/sympy,grevutiu-gabriel/sympy,rahuldan/sympy,wanglongqi/sympy,bukzor/sympy,drufat/sympy,sahilshekhawat/sympy,AunShiLord/sympy,flacjacket/sympy,toolforger/sympy,Gadal/sympy,skidzo/sympy,kaushik94/sympy,farhaanbukhsh/sympy,emon10005/sympy,bukzor/sympy,jbbskinny/sympy,rahuldan/sympy,AkademieOlympia/sympy,sunny94/temp,yashsharan/sympy,yukoba/sympy,hargup/sympy,atsao72/sympy,skidzo/sympy,kumarkrishna/sympy,cswiercz/sympy,souravsingh/sympy,dqnykamp/sympy,chaffra/sympy,lidavidm/sympy,lindsayad/sympy,sahmed95/sympy,Davidjohnwilson/sympy,MechCoder/sympy,jerli/sympy,skidzo/sympy,jamesblunt/sympy,drufat/sympy,farhaanbukhsh/sympy,abloomston/sympy,abhiii5459/sympy,MechCoder/sympy,kaushik94/sympy,cswiercz/sympy,Designist/sympy,liangjiaxing/sympy,diofant/diofant,mafiya69/sympy,kmacinnis/sympy,kaushik94/sympy,jamesblunt/sympy,hrashk/sympy,sampadsaha5/sympy,aktech/sympy,madan96/sympy,meghana1995/sympy,shikil/sympy,Arafatk/sympy,amitjamadagni/sympy,Shaswat27/sympy,maniteja123/sympy,lidavidm/sympy,Vishluck/sympy,garvitr/sympy,asm666/sympy,shikil/sympy,cswiercz/sympy,Titan-C/sympy,mcdaniel67/sympy,garvitr/sympy,sahmed95/sympy,liangjiaxing/sympy,Davidjohnwilson/sympy,Arafatk/sympy,VaibhavAgarwalVA/sympy,vipulroxx/sympy,shipci/sympy,MridulS/sympy,toolforger/sympy,kumarkrishna/sympy,AunShiLord/sympy,Davidjohnwilson/sympy,wanglongqi/sympy,Mitchkoens/sympy,iamutkarshtiwari/sympy,atreyv/sympy,aktech/sympy,pbrady/sympy,souravsingh/sympy,Curious72/sympy,dqnykamp/sympy,moble/sympy,VaibhavAgarwalVA/sympy,ga7g08/sympy,ahhda/sympy,ahhda/sympy,wyom/sympy,Mitchkoens/sympy,atsao72/sympy,souravsingh/sympy,pandeyadarsh/sympy,MechCoder/sympy,madan96/sympy,atreyv/sympy,kumarkrishna/sympy,dqnykamp/sympy,AkademieOlympia/sympy,Titan-C/sympy,rahuldan/sympy,oliverlee/sympy,Curious72/sympy,postvakje/sympy,chaffra/sympy,cccfran/sympy,jamesblunt/sympy,debugger22/sympy,ChristinaZografou/sympy,bukzor/sympy,yukoba/sympy,hargup/sympy,asm666/sympy,saurabhjn76/sympy,iamutkarshtiwari/sympy,abloomston/sympy,Shaswat27/sympy,Sumith1896/sympy,saurabhjn76/sympy,grevutiu-gabriel/sympy,mafiya69/sympy,ga7g08/sympy,atreyv/sympy,Shaswat27/sympy,kevalds51/sympy,Sumith1896/sympy,Titan-C/sympy,jaimahajan1997/sympy,drufat/sympy,maniteja123/sympy,hargup/sympy,Mitchkoens/sympy,moble/sympy,emon10005/sympy,shipci/sympy,hrashk/sympy,iamutkarshtiwari/sympy,mafiya69/sympy,asm666/sympy,ChristinaZografou/sympy,MridulS/sympy,pbrady/sympy,beni55/sympy,meghana1995/sympy,Vishluck/sympy,cccfran/sympy,sampadsaha5/sympy,ahhda/sympy,ga7g08/sympy,pandeyadarsh/sympy,kevalds51/sympy,sunny94/temp,saurabhjn76/sympy,srjoglekar246/sympy,kmacinnis/sympy,beni55/sympy,Curious72/sympy,AunShiLord/sympy,sampadsaha5/sympy,jaimahajan1997/sympy,debugger22/sympy,cccfran/sympy,vipulroxx/sympy,pandeyadarsh/sympy,abhiii5459/sympy,wanglongqi/sympy,AkademieOlympia/sympy,skirpichev/omg,yashsharan/sympy,kaichogami/sympy