10.64: Difference between revisions

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! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica
! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica
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| [https://dlmf.nist.gov/10.64.E1 10.64.E1] || [[Item:Q3829|<math>\Kelvinber{n}@{x\sqrt{2}} = \frac{(-1)^{n}}{\pi}\int_{0}^{\pi}\cos@{x\sin@@{t}-nt}\cosh@{x\sin@@{t}}\diff{t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Kelvinber{n}@{x\sqrt{2}} = \frac{(-1)^{n}}{\pi}\int_{0}^{\pi}\cos@{x\sin@@{t}-nt}\cosh@{x\sin@@{t}}\diff{t}</syntaxhighlight> || <math>\realpart@@{(n+k+1)} > 0</math> || <syntaxhighlight lang=mathematica>KelvinBer(n, x*sqrt(2)) = ((- 1)^(n))/(Pi)*int(cos(x*sin(t)- n*t)*cosh(x*sin(t)), t = 0..Pi)</syntaxhighlight> || <syntaxhighlight lang=mathematica>KelvinBer[n, x*Sqrt[2]] == Divide[(- 1)^(n),Pi]*Integrate[Cos[x*Sin[t]- n*t]*Cosh[x*Sin[t]], {t, 0, Pi}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Successful [Tested: 9] || Skipped - Because timed out
| [https://dlmf.nist.gov/10.64.E1 10.64.E1] || <math qid="Q3829">\Kelvinber{n}@{x\sqrt{2}} = \frac{(-1)^{n}}{\pi}\int_{0}^{\pi}\cos@{x\sin@@{t}-nt}\cosh@{x\sin@@{t}}\diff{t}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Kelvinber{n}@{x\sqrt{2}} = \frac{(-1)^{n}}{\pi}\int_{0}^{\pi}\cos@{x\sin@@{t}-nt}\cosh@{x\sin@@{t}}\diff{t}</syntaxhighlight> || <math>\realpart@@{(n+k+1)} > 0</math> || <syntaxhighlight lang=mathematica>KelvinBer(n, x*sqrt(2)) = ((- 1)^(n))/(Pi)*int(cos(x*sin(t)- n*t)*cosh(x*sin(t)), t = 0..Pi)</syntaxhighlight> || <syntaxhighlight lang=mathematica>KelvinBer[n, x*Sqrt[2]] == Divide[(- 1)^(n),Pi]*Integrate[Cos[x*Sin[t]- n*t]*Cosh[x*Sin[t]], {t, 0, Pi}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Successful [Tested: 9] || Skipped - Because timed out
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| [https://dlmf.nist.gov/10.64.E2 10.64.E2] || [[Item:Q3830|<math>\Kelvinbei{n}@{x\sqrt{2}} = \frac{(-1)^{n}}{\pi}\int_{0}^{\pi}\sin@{x\sin@@{t}-nt}\sinh@{x\sin@@{t}}\diff{t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Kelvinbei{n}@{x\sqrt{2}} = \frac{(-1)^{n}}{\pi}\int_{0}^{\pi}\sin@{x\sin@@{t}-nt}\sinh@{x\sin@@{t}}\diff{t}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>KelvinBei(n, x*sqrt(2)) = ((- 1)^(n))/(Pi)*int(sin(x*sin(t)- n*t)*sinh(x*sin(t)), t = 0..Pi)</syntaxhighlight> || <syntaxhighlight lang=mathematica>KelvinBei[n, x*Sqrt[2]] == Divide[(- 1)^(n),Pi]*Integrate[Sin[x*Sin[t]- n*t]*Sinh[x*Sin[t]], {t, 0, Pi}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Successful [Tested: 9] || Skipped - Because timed out
| [https://dlmf.nist.gov/10.64.E2 10.64.E2] || <math qid="Q3830">\Kelvinbei{n}@{x\sqrt{2}} = \frac{(-1)^{n}}{\pi}\int_{0}^{\pi}\sin@{x\sin@@{t}-nt}\sinh@{x\sin@@{t}}\diff{t}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Kelvinbei{n}@{x\sqrt{2}} = \frac{(-1)^{n}}{\pi}\int_{0}^{\pi}\sin@{x\sin@@{t}-nt}\sinh@{x\sin@@{t}}\diff{t}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>KelvinBei(n, x*sqrt(2)) = ((- 1)^(n))/(Pi)*int(sin(x*sin(t)- n*t)*sinh(x*sin(t)), t = 0..Pi)</syntaxhighlight> || <syntaxhighlight lang=mathematica>KelvinBei[n, x*Sqrt[2]] == Divide[(- 1)^(n),Pi]*Integrate[Sin[x*Sin[t]- n*t]*Sinh[x*Sin[t]], {t, 0, Pi}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Successful [Tested: 9] || Skipped - Because timed out
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Latest revision as of 11:28, 28 June 2021


DLMF Formula Constraints Maple Mathematica Symbolic
Maple 		Symbolic
Mathematica 		Numeric
Maple 		Numeric
Mathematica
10.64.E1 ber n ⁡ ( x ⁢ 2 ) = ( - 1 ) n π ⁢ ∫ 0 π cos ⁡ ( x ⁢ sin ⁡ t - n ⁢ t ) ⁢ cosh ⁡ ( x ⁢ sin ⁡ t ) ⁢ d t Kelvin-ber 𝑛 𝑥 2 superscript 1 𝑛 𝜋 superscript subscript 0 𝜋 𝑥 𝑡 𝑛 𝑡 𝑥 𝑡 𝑡 {\displaystyle{\displaystyle\operatorname{ber}_{n}\left(x\sqrt{2}\right)=\frac% {(-1)^{n}}{\pi}\int_{0}^{\pi}\cos\left(x\sin t-nt\right)\cosh\left(x\sin t% \right)\mathrm{d}t}}
\Kelvinber{n}@{x\sqrt{2}} = \frac{(-1)^{n}}{\pi}\int_{0}^{\pi}\cos@{x\sin@@{t}-nt}\cosh@{x\sin@@{t}}\diff{t}		 ℜ ⁡ ( n + k + 1 ) > 0 𝑛 𝑘 1 0 {\displaystyle{\displaystyle\Re(n+k+1)>0}} 
KelvinBer(n, x*sqrt(2)) = ((- 1)^(n))/(Pi)*int(cos(x*sin(t)- n*t)*cosh(x*sin(t)), t = 0..Pi)

KelvinBer[n, x*Sqrt[2]] == Divide[(- 1)^(n),Pi]*Integrate[Cos[x*Sin[t]- n*t]*Cosh[x*Sin[t]], {t, 0, Pi}, GenerateConditions->None]
Failure Aborted Successful [Tested: 9] Skipped - Because timed out
10.64.E2 bei n ⁡ ( x ⁢ 2 ) = ( - 1 ) n π ⁢ ∫ 0 π sin ⁡ ( x ⁢ sin ⁡ t - n ⁢ t ) ⁢ sinh ⁡ ( x ⁢ sin ⁡ t ) ⁢ d t Kelvin-bei 𝑛 𝑥 2 superscript 1 𝑛 𝜋 superscript subscript 0 𝜋 𝑥 𝑡 𝑛 𝑡 𝑥 𝑡 𝑡 {\displaystyle{\displaystyle\operatorname{bei}_{n}\left(x\sqrt{2}\right)=\frac% {(-1)^{n}}{\pi}\int_{0}^{\pi}\sin\left(x\sin t-nt\right)\sinh\left(x\sin t% \right)\mathrm{d}t}}
\Kelvinbei{n}@{x\sqrt{2}} = \frac{(-1)^{n}}{\pi}\int_{0}^{\pi}\sin@{x\sin@@{t}-nt}\sinh@{x\sin@@{t}}\diff{t}		 

KelvinBei(n, x*sqrt(2)) = ((- 1)^(n))/(Pi)*int(sin(x*sin(t)- n*t)*sinh(x*sin(t)), t = 0..Pi)

KelvinBei[n, x*Sqrt[2]] == Divide[(- 1)^(n),Pi]*Integrate[Sin[x*Sin[t]- n*t]*Sinh[x*Sin[t]], {t, 0, Pi}, GenerateConditions->None]
Failure Aborted Successful [Tested: 9] Skipped - Because timed out
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