Asymptotic Approximations - 2.3 Integrals of a Real Variable

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DLMF Formula Constraints Maple Mathematica Symbolic
Maple 		Symbolic
Mathematica 		Numeric
Maple 		Numeric
Mathematica
2.3#Ex4 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle b_{0} = \frac{q_{0}}{\mu p_{0}^{\lambda/\mu}}}
b_{0} = \frac{q_{0}}{\mu p_{0}^{\lambda/\mu}}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
b[0] = (q[0])/(mu*(p[0])^(lambda/mu))
 
Subscript[b, 0] == Divide[Subscript[q, 0],\[Mu]*(Subscript[p, 0])^(\[Lambda]/\[Mu])]
 Skipped - no semantic math Skipped - no semantic math - -
2.3#Ex5 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle b_{1} = \left(\frac{q_{1}}{\mu}-\frac{(\lambda+1)p_{1}q_{0}}{\mu^{2}p_{0}}\right)\frac{1}{p_{0}^{(\lambda+1)/\mu}}}
b_{1} = \left(\frac{q_{1}}{\mu}-\frac{(\lambda+1)p_{1}q_{0}}{\mu^{2}p_{0}}\right)\frac{1}{p_{0}^{(\lambda+1)/\mu}}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
b[1] = ((q[1])/(mu)-((lambda + 1)*p[1]*q[0])/((mu)^(2)* p[0]))*(1)/((p[0])^((lambda + 1)/mu))
 
Subscript[b, 1] == (Divide[Subscript[q, 1],\[Mu]]-Divide[(\[Lambda]+ 1)*Subscript[p, 1]*Subscript[q, 0],\[Mu]^(2)* Subscript[p, 0]])*Divide[1,(Subscript[p, 0])^((\[Lambda]+ 1)/\[Mu])]
 Skipped - no semantic math Skipped - no semantic math - -
2.3#Ex6 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle b_{2} = \left(\frac{q_{2}}{\mu}-\frac{(\lambda+2)(p_{1}q_{1}+p_{2}q_{0})}{\mu^{2}p_{0}}+\frac{(\lambda+2)(\lambda+\mu+2)p_{1}^{2}q_{0}}{2\mu^{3}p_{0}^{2}}\right)\frac{1}{p_{0}^{(\lambda+2)/\mu}}}
b_{2} = \left(\frac{q_{2}}{\mu}-\frac{(\lambda+2)(p_{1}q_{1}+p_{2}q_{0})}{\mu^{2}p_{0}}+\frac{(\lambda+2)(\lambda+\mu+2)p_{1}^{2}q_{0}}{2\mu^{3}p_{0}^{2}}\right)\frac{1}{p_{0}^{(\lambda+2)/\mu}}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
b[2] = ((q[2])/(mu)-((lambda + 2)*(p[1]*q[1]+ p[2]*q[0]))/((mu)^(2)* p[0])+((lambda + 2)*(lambda + mu + 2)*(p[1])^(2)*q[0])/(2*(mu)^(3)* (p[0])^(2)))*(1)/((p[0])^((lambda + 2)/mu))
 
Subscript[b, 2] == (Divide[Subscript[q, 2],\[Mu]]-Divide[(\[Lambda]+ 2)*(Subscript[p, 1]*Subscript[q, 1]+ Subscript[p, 2]*Subscript[q, 0]),\[Mu]^(2)* Subscript[p, 0]]+Divide[(\[Lambda]+ 2)*(\[Lambda]+ \[Mu]+ 2)*(Subscript[p, 1])^(2)*Subscript[q, 0],2*\[Mu]^(3)* (Subscript[p, 0])^(2)])*Divide[1,(Subscript[p, 0])^((\[Lambda]+ 2)/\[Mu])]
 Skipped - no semantic math Skipped - no semantic math - -
2.3.E18 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle b_{s} = \frac{1}{\mu}\Residue_{t=a}\left[\frac{q(t)}{(p(t)-p(a))^{(\lambda+s)/\mu}}\right]}
b_{s} = \frac{1}{\mu}\Residue_{t=a}\left[\frac{q(t)}{(p(t)-p(a))^{(\lambda+s)/\mu}}\right]		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
b[s] = (1)/(mu)*[t = a]*((q(t))/((p(t)- p(a))^((lambda + s)/mu)))
 
Subscript[b, s] == Divide[1,\[Mu]]*Subscript[, t == a]*(Divide[q[t],(p[t]- p[a])^((\[Lambda]+ s)/\[Mu])])
 Skipped - no semantic math Skipped - no semantic math - -
2.3.E25 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle p(\alpha,t) = \tfrac{1}{2}w^{2}-aw+b}
p(\alpha,t) = \tfrac{1}{2}w^{2}-aw+b		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
p(alpha , t) = (1)/(2)*(w)^(2)- a*w + b
 
p[\[Alpha], t] == Divide[1,2]*(w)^(2)- a*w + b
 Skipped - no semantic math Skipped - no semantic math - -
2.3#Ex7 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a = (2p(\alpha,0)-2p(\alpha,\alpha))^{1/2}}
a = (2p(\alpha,0)-2p(\alpha,\alpha))^{1/2}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
a = (2*p(alpha , 0)- 2*p(alpha , alpha))^(1/2)
 
a == (2*p[\[Alpha], 0]- 2*p[\[Alpha], \[Alpha]])^(1/2)
 Skipped - no semantic math Skipped - no semantic math - -
2.3#Ex8 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle b = p(\alpha,0)}
b = p(\alpha,0)		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
b = p(alpha , 0)
 
b == p[\[Alpha], 0]
 Skipped - no semantic math Skipped - no semantic math - -
2.3.E27 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w = (2p(\alpha,0)-2p(\alpha,\alpha))^{1/2}+(2p(\alpha,t)-2p(\alpha,\alpha))^{1/2}}
w = (2p(\alpha,0)-2p(\alpha,\alpha))^{1/2}+(2p(\alpha,t)-2p(\alpha,\alpha))^{1/2}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
w = (2*p(alpha , 0)- 2*p(alpha , alpha))^(1/2)+(2*p(alpha , t)- 2*p(alpha , alpha))^(1/2)
 
w == (2*p[\[Alpha], 0]- 2*p[\[Alpha], \[Alpha]])^(1/2)+(2*p[\[Alpha], t]- 2*p[\[Alpha], \[Alpha]])^(1/2)
 Skipped - no semantic math Skipped - no semantic math - -
2.3.E28 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv{w}{t} = +\frac{1}{(2p(\alpha,t)-2p(\alpha,\alpha))^{1/2}}\pderiv{p(\alpha,t)}{t}}
\deriv{w}{t} = +\frac{1}{(2p(\alpha,t)-2p(\alpha,\alpha))^{1/2}}\pderiv{p(\alpha,t)}{t}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
diff(w, t) = +(1)/((2*p(alpha , t)- 2*p(alpha , alpha))^(1/2))*diff(p(alpha , t), t)

D[w, t] == +Divide[1,(2*p[\[Alpha], t]- 2*p[\[Alpha], \[Alpha]])^(1/2)]*D[p[\[Alpha], t], t]
Error Failure - Error
2.3.E28 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv{w}{t} = -\frac{1}{(2p(\alpha,t)-2p(\alpha,\alpha))^{1/2}}\pderiv{p(\alpha,t)}{t}}
\deriv{w}{t} = -\frac{1}{(2p(\alpha,t)-2p(\alpha,\alpha))^{1/2}}\pderiv{p(\alpha,t)}{t}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
diff(w, t) = -(1)/((2*p(alpha , t)- 2*p(alpha , alpha))^(1/2))*diff(p(alpha , t), t)

D[w, t] == -Divide[1,(2*p[\[Alpha], t]- 2*p[\[Alpha], \[Alpha]])^(1/2)]*D[p[\[Alpha], t], t]
Error Failure - Error
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