Bessel Functions - 10.64 Integral Representations

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
10.64.E1	${\displaystyle{\displaystyle\operatorname{ber}_{n}\left(x\sqrt{2}\right)=\frac{(-1)^{n}}{\pi}\int_{0}^{\pi}\cos\left(x\sin t-nt\right)\cosh\left(x\sin t\right)\mathrm{d}t}}$ \Kelvinber{n}@{x\sqrt{2}} = \frac{(-1)^{n}}{\pi}\int_{0}^{\pi}\cos@{x\sin@@{t}-nt}\cosh@{x\sin@@{t}}\diff{t}	${\displaystyle{\displaystyle\Re(n+k+1)>0}}$	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	${\displaystyle{\displaystyle\operatorname{bei}_{n}\left(x\sqrt{2}\right)=\frac{(-1)^{n}}{\pi}\int_{0}^{\pi}\sin\left(x\sin t-nt\right)\sinh\left(x\sin t\right)\mathrm{d}t}}$ \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