Re: Complex bessel function

*To*: mathgroup at smc.vnet.net*Subject*: [mg75186] Re: Complex bessel function*From*: dimitris <dimmechan at yahoo.com>*Date*: Fri, 20 Apr 2007 00:31:50 -0400 (EDT)*References*: <f079np$46c$1@smc.vnet.net>

$VersionNumber 5=2E2 In[1]:= f[a_, b_] := BesselI[0, a*Sqrt[I] + b] In[2]:= ComplexExpand[f[1, 2]] Out[2]= I*Im[BesselI[0, 2 + (-1)^(1/4)]] + Re[BesselI[0, 2 + (-1)^(1/4)]] In[4]:= (ComplexExpand[#1, TargetFunctions -> {Abs, Arg}] & )[f[1, 2]] Out[4]= Abs[BesselI[0, 2 + (-1)^(1/4)]]*Cos[Arg[BesselI[0, 2 + (-1)^(1/4)]]] + I*Abs[BesselI[0, 2 + (-1)^(1/4)]]* Sin[Arg[BesselI[0, 2 + (-1)^(1/4)]]] In[3]:= ComplexExpand[f[a, b]] Out[3]= I*Im[BesselI[0, (-1)^(1/4)*a + b]] + Re[BesselI[0, (-1)^(1/4)*a + b]] In[5]:= (ComplexExpand[#1, TargetFunctions -> {Abs, Arg}] & )[f[a, b]] Out[5]= Abs[BesselI[0, (-1)^(1/4)*a + b]]*Cos[Arg[BesselI[0, (-1)^(1/4)*a + b]]] + I*Abs[BesselI[0, (-1)^(1/4)*a + b]]* Sin[Arg[BesselI[0, (-1)^(1/4)*a + b]]] ??? =CF/=C7 Grasley, Zachary =DD=E3=F1=E1=F8=E5: > I am currently trying to isolate the real and imaginary components of > first and second order modified Bessel functions. For example, I have a > function expressed as > > > > F=BesselI[0,sqrt(i)*a+b], where i is the imaginary unit. Both a and b > are positive real. I need to separate out the real and imaginary > components of F symbolically. I have tried Re, Im, ComplexExpand, I > have used Assuming to define a and b as real and 0<a<infinity and > 0<b<infinity. I have tried ComplexExpand. I have tried Refine[Im[F]]. > I loaded the package ReIm. > > > > All of these functions do a fine job separating the real and imaginary > components when I provide numeric values for a and b, but are unable to > solve symbolically. I thought Refine was supposed to solve symbolically > as if a numeric value has been assigned to the variables (with the value > range of the variable defined by Assuming or the assumptions listed in > Refine)? Am I missing some simple trick to solve this symbolically, or > is this not possible? > > > > Thanks in advance! > > Zach