Bernoulli and Euler Polynomials - 24.12 Zeros

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DLMF Formula Constraints Maple Mathematica Symbolic
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24.12.E1 1 2 ≀ x 1 ( n ) 1 2 superscript subscript π‘₯ 1 𝑛 {\displaystyle{\displaystyle\tfrac{1}{2}\leq x_{1}^{(n)}}}
\tfrac{1}{2} \leq x_{1}^{(n)}

(1)/(2) <= (x[1])^(n)
Divide[1,2] <= (Subscript[x, 1])^(n)
Skipped - no semantic math Skipped - no semantic math - -
24.12.E2 3 4 + 1 2 n + 2 ⁒ Ο€ < x 1 ( n ) 3 4 1 superscript 2 𝑛 2 πœ‹ subscript superscript π‘₯ 𝑛 1 {\displaystyle{\displaystyle\frac{3}{4}+\frac{1}{2^{n+2}\pi}<x^{(n)}_{1}}}
\frac{3}{4}+\frac{1}{2^{n+2}\pi} < x^{(n)}_{1}

(3)/(4)+(1)/((2)^(n + 2)* Pi) < (x[1])^(n)
Divide[3,4]+Divide[1,(2)^(n + 2)* Pi] < (Subscript[x, 1])^(n)
Skipped - no semantic math Skipped - no semantic math - -
24.12.E7 1 2 ≀ y 1 ( n ) 1 2 subscript superscript 𝑦 𝑛 1 {\displaystyle{\displaystyle\tfrac{1}{2}\leq y^{(n)}_{1}}}
\tfrac{1}{2} \leq y^{(n)}_{1}

(1)/(2) <= (y[1])^(n)
Divide[1,2] <= (Subscript[y, 1])^(n)
Skipped - no semantic math Skipped - no semantic math - -
24.12.E9 3 2 - Ο€ n + 1 3 ⁒ ( n ! ) < y 2 ( n ) 3 2 superscript πœ‹ 𝑛 1 3 𝑛 subscript superscript 𝑦 𝑛 2 {\displaystyle{\displaystyle\frac{3}{2}-\frac{\pi^{n+1}}{3(n!)}<y^{(n)}_{2}}}
\frac{3}{2}-\frac{\pi^{n+1}}{3(n!)} < y^{(n)}_{2}

(3)/(2)-((Pi)^(n + 1))/(3*(factorial(n))) < (y[2])^(n)
Divide[3,2]-Divide[(Pi)^(n + 1),3*((n)!)] < (Subscript[y, 2])^(n)
Skipped - no semantic math Skipped - no semantic math - -
24.12.E10 3 2 < y 2 ( n ) 3 2 subscript superscript 𝑦 𝑛 2 {\displaystyle{\displaystyle\frac{3}{2}<y^{(n)}_{2}}}
\frac{3}{2} < y^{(n)}_{2}

(3)/(2) < (y[2])^(n)
Divide[3,2] < (Subscript[y, 2])^(n)
Skipped - no semantic math Skipped - no semantic math - -