Opened 7 years ago
Closed 4 years ago
#12628 closed defect (fixed)
Integration of Product of Sin(nz)/(nz) says divergent, but is not divergent
Reported by: | dkrenn | Owned by: | burcin |
---|---|---|---|
Priority: | major | Milestone: | sage-6.4 |
Component: | calculus | Keywords: | integration, divergent, infinity |
Cc: | Merged in: | ||
Authors: | Daniel Krenn | Reviewers: | Ralf Stephan |
Report Upstream: | Reported upstream. Developers acknowledge bug. | Work issues: | |
Branch: | c3fb2ff (Commits) | Commit: | c3fb2ff1a2ddefb21dca15a0f1b8e2f971fc4caa |
Dependencies: | Stopgaps: |
Description (last modified by )
We have
sage: var('z,n') (z, n) sage: f(z,n) = sin(n*z)/(n*z) sage: integrate(f(z,1)*f(z,3)*f(z,5)*f(z,7),z,0,oo) Traceback (most recent call last) ... ValueError: Integral is divergent.
but the value of that integral is 22/315*pi
, see, for example, evaluations in Mathematica below.
Splitting the integral gives
sage: integrate(f(z,1)*f(z,3)*f(z,5)*f(z,7),z,0,1) 1/105*integrate(sin(3*z)*sin(5*z)*sin(7*z)*sin(z)/z^4, z, 0, 1) sage: integrate(f(z,1)*f(z,3)*f(z,5)*f(z,7),z,1,oo) 256/105*I*gamma(-3, -16*I) - 49/30*I*gamma(-3, -14*I) - 25/42*I*gamma(-3, -10*I) + 32/105*I*gamma(-3, -8*I) - 9/70*I*gamma(-3, -6*I) + 4/105*I*gamma(-3, -4*I) - 1/210*I*gamma(-3, -2*I) + 1/210*I*gamma(-3, 2*I) - 4/105*I*gamma(-3, 4*I) + 9/70*I*gamma(-3, 6*I) - 32/105*I*gamma(-3, 8*I) + 25/42*I*gamma(-3, 10*I) + 49/30*I*gamma(-3, 14*I) - 256/105*I*gamma(-3, 16*I) + 1/2520
so we see that the integral from 0 to 1 is not evaluated.
Here are some more examples and the comparison to Mathematica:
sage: var('z,n') (z, n) sage: f(z,n) = sin(n*z)/(n*z) sage: integrate(f(z,1),z,0,oo) 1/2*pi sage: integrate(f(z,1)*f(z,3),z,0,oo) 1/6*pi sage: integrate(f(z,1)*f(z,3)*f(z,5),z,0,oo) 1/10*pi sage: integrate(f(z,1)*f(z,3)*f(z,5)*f(z,7),z,0,oo) Traceback (most recent call last) ... ValueError: Integral is divergent. sage: integrate(f(z,1)*f(z,3)*f(z,5)*f(z,7)*f(z,9),z,0,oo) 3677/72576*pi sage: integrate(f(z,1)*f(z,3)*f(z,5)*f(z,7)*f(z,9)*f(z,11),z,0,oo) Traceback (most recent call last) ... ValueError: Integral is divergent. sage: integrate(f(z,1)*f(z,3)*f(z,5)*f(z,7)*f(z,9)*f(z,11)*f(z,13),z,0,oo) 193359161/6227020800*pi sage: integrate(f(z,1)*f(z,3)*f(z,5)*f(z,7)*f(z,9)*f(z,11)*f(z,13)*f(z,15),z,0,oo) Traceback (most recent call last) ... ValueError: Integral is divergent.
In[1]:= f[z_,n_]:=Sin[n z]/(n z) In[2]:= Integrate[f[z,1],{z,0,Infinity}] Pi Out[2]= -- 2 In[3]:= Integrate[f[z,1]*f[z,3],{z,0,Infinity}] Pi Out[3]= -- 6 In[4]:= Integrate[f[z,1]*f[z,3]*f[z,5],{z,0,Infinity}] Pi Out[4]= -- 10 In[5]:= Integrate[f[z,1]*f[z,3]*f[z,5]*f[z,7],{z,0,Infinity}] 22 Pi Out[5]= ----- 315 In[6]:= Integrate[f[z,1]*f[z,3]*f[z,5]*f[z,7]*f[z,9],{z,0,Infinity}] 3677 Pi Out[6]= ------- 72576 In[7]:= Integrate[f[z,1]*f[z,3]*f[z,5]*f[z,7]*f[z,9]*f[z,11],{z,0,Infinity}] 48481 Pi Out[7]= -------- 1247400 In[8]:= Integrate[f[z,1]*f[z,3]*f[z,5]*f[z,7]*f[z,9]*f[z,11]*f[z,13],{z,0,Infinity}] 193359161 Pi Out[8]= ------------ 6227020800 In[9]:= Integrate[f[z,1]*f[z,3]*f[z,5]*f[z,7]*f[z,9]*f[z,11]*f[z,13]*f[z,15],{z,0,Infinity}] 5799919 Pi Out[9]= ---------- 227026800
Change History (13)
comment:1 Changed 7 years ago by
- Description modified (diff)
comment:2 Changed 7 years ago by
comment:3 Changed 7 years ago by
- Report Upstream changed from N/A to Reported upstream. Little or no feedback.
comment:4 Changed 7 years ago by
- Report Upstream changed from Reported upstream. Little or no feedback. to Reported upstream. Developers acknowledge bug.
comment:5 Changed 6 years ago by
- Milestone changed from sage-5.11 to sage-5.12
comment:6 Changed 5 years ago by
- Milestone changed from sage-6.1 to sage-6.2
comment:7 Changed 5 years ago by
- Milestone changed from sage-6.2 to sage-6.3
comment:8 Changed 5 years ago by
- Milestone changed from sage-6.3 to sage-6.4
comment:9 follow-up: ↓ 11 Changed 4 years ago by
This works now in Sage 6.5beta4, so just a doctest is needed.
comment:10 Changed 4 years ago by
- Branch set to u/dkrenn/t/12628
comment:11 in reply to: ↑ 9 Changed 4 years ago by
- Commit set to c3fb2ff1a2ddefb21dca15a0f1b8e2f971fc4caa
- Status changed from new to needs_review
comment:12 Changed 4 years ago by
- Reviewers set to Ralf Stephan
- Status changed from needs_review to positive_review
Is fine, thanks.
comment:13 Changed 4 years ago by
- Branch changed from u/dkrenn/t/12628 to c3fb2ff1a2ddefb21dca15a0f1b8e2f971fc4caa
- Resolution set to fixed
- Status changed from positive_review to closed
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Naturally, this is straight from Maxima.
That is kind of weird, the even/odd (well, mod 4) issue.
This is now on the Maxima bug tracker.