Goodwin–Staton integral - Alchetron, the free social encyclopedia

In mathematics the Goodwin–Staton integral is defined as :

G ( z ) = ∫ 0 ∞ e − t 2 t + z d t

It satisfies the following third-order nonlinear differential equation：

4 w ( z ) + 8 z d d z w ( z ) + ( 2 + 2 z 2 ) d 2 d z 2 w ( z ) + z d 3 d z 3 w ( z ) = 0

Symmetry

G ( − z ) = − G ( z ) G ( z ) = ( 1 − γ − ln ⁡ ( z 2 ) − i csgn ⁡ ( i z 2 ) π + 2 i π z + ( − 2 + γ + ln ⁡ ( z 2 ) + i csgn ⁡ ( i z 2 ) π ) z 2 − 4 i 3 π z 3 + ( 5 4 − 1 2 γ − 1 2 ln ⁡ ( z 2 ) − 1 2 i csgn ⁡ ( i z 2 ) π ) z 4 + O ( z 5 ) )

References

Goodwin–Staton integral Wikipedia

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