Integrals with Coalescing Saddles - 36.12 Uniform Approximation of Integrals

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DLMF Formula Constraints Maple Mathematica Symbolic
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36.12.E9 P m ⁒ n ⁒ ( 𝐲 ) = ( t n ⁒ ( 𝐱 ⁒ ( 𝐲 ) ) ) K + 1 + βˆ‘ l = m + 2 K l K + 2 ⁒ x l ⁒ ( 𝐲 ) ⁒ ( t n ⁒ ( 𝐱 ⁒ ( 𝐲 ) ) ) l - 1 subscript 𝑃 π‘š 𝑛 𝐲 superscript subscript 𝑑 𝑛 𝐱 𝐲 𝐾 1 superscript subscript 𝑙 π‘š 2 𝐾 𝑙 𝐾 2 subscript π‘₯ 𝑙 𝐲 superscript subscript 𝑑 𝑛 𝐱 𝐲 𝑙 1 {\displaystyle{\displaystyle P_{mn}(\mathbf{y})=(t_{n}(\mathbf{x}(\mathbf{y}))% )^{K+1}+\sum_{l=m+2}^{K}\frac{l}{K+2}x_{l}(\mathbf{y})(t_{n}(\mathbf{x}(% \mathbf{y})))^{l-1}}}
P_{mn}(\mathbf{y}) = (t_{n}(\mathbf{x}(\mathbf{y})))^{K+1}+\sum_{l=m+2}^{K}\frac{l}{K+2}x_{l}(\mathbf{y})(t_{n}(\mathbf{x}(\mathbf{y})))^{l-1}

P[m, n](y) = (t[n](x(y)))^(K + 1)+ sum((l)/(K + 2)*x[l](y)*(t[n](x(y)))^(l - 1), l = m + 2..K)
Subscript[P, m, n][y] == (Subscript[t, n][x[y]])^(K + 1)+ Sum[Divide[l,K + 2]*Subscript[x, l][y]*(Subscript[t, n][x[y]])^(l - 1), {l, m + 2, K}, GenerateConditions->None]
Failure Failure Skipped - Because timed out Skipped - Because timed out