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J. M.'s missing motivation ♦
J. M.'s missing motivation ♦
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Taking the directional limits will reveal Mathematica's conventions:

Assuming[x > 1, Limit[EllipticK[x + I ε], ε -> 0, Direction -> 1]]

EllipticK[x]

Assuming[x > 1, Limit[EllipticK[x + I ε], ε]ε -> 0, Direction -> -1]]

2 I EllipticK[1 - x] + EllipticK[x]

Taking the directional limits will reveal Mathematica's conventions:

Assuming[x > 1, Limit[EllipticK[x + I ε], ε -> 0, Direction -> 1]]

EllipticK[x]

Assuming[x > 1, Limit[EllipticK[x + I ε], ε] -> 0, Direction -> -1]]

2 I EllipticK[1 - x] + EllipticK[x]

Taking the directional limits will reveal Mathematica's conventions:

Assuming[x > 1, Limit[EllipticK[x + I ε], ε -> 0, Direction -> 1]]

EllipticK[x]

Assuming[x > 1, Limit[EllipticK[x + I ε], ε -> 0, Direction -> -1]]

2 I EllipticK[1 - x] + EllipticK[x]

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QuantumDot
QuantumDot
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Taking the directional limits will reveal Mathematica's conventions:

Assuming[x > 1, Limit[EllipticK[x + I ε], ε -> 0, Direction -> 1]]

EllipticK[x]

Assuming[x > 1, Limit[EllipticK[x + I ε], ε] -> 0, Direction -> -1]]

2 I EllipticK[1 - x] + EllipticK[x]