Fresnel integral C: Integration (formula 06.33.21.0051)

FresnelC

$Mathematica Notation$

Gamma, Beta, Erf

FresnelC[z]

Integration

Indefinite integration

Involving one direct function and elementary functions

Involving power, exponential and trigonometric functions

Involving power, exp and sin

http://functions.wolfram.com/06.33.21.0051.01

Input Form

Integrate[z^(\[Alpha] - 1) E^(b z) Sin[c z] FresnelC[a z], z] == ((I a z^\[Alpha])/2) Sum[(((-1)^k Pi^(2 k) a^(4 k))/ (2^(2 k) ((4 k + 1) (2 k)!))) (((b - I c)^(-4 k - 1) Gamma[1 + 4 k + \[Alpha], (-(b - I c)) z])/ ((-b + I c) z)^\[Alpha] - ((b + I c)^(-4 k - 1) Gamma[1 + 4 k + \[Alpha], (-(b + I c)) z])/((-b - I c) z)^\[Alpha]), {k, 0, Infinity}]

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2001-10-29