The Sine Product Formula and the Gamma Function
The Sine Product Formula and the Gamma Function
The Sine Product Formula and the Gamma Function
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<strong>Sine</strong> <strong>and</strong> <strong>Gamma</strong> <strong>Function</strong>s<br />
<strong>Sine</strong> <strong>and</strong> <strong>Gamma</strong> <strong>Function</strong>s<br />
Proof:<br />
Proof:<br />
)<br />
(<br />
1)sin<br />
(<br />
)<br />
(<br />
1)<br />
(<br />
)<br />
sin<br />
(<br />
1)<br />
(<br />
)<br />
(<br />
1)<br />
(<br />
1))<br />
(<br />
)sin(<br />
(<br />
1)<br />
(<br />
1)<br />
(<br />
1)<br />
(<br />
)<br />
(<br />
)<br />
(<br />
1)<br />
(<br />
x<br />
x<br />
x<br />
x<br />
x<br />
x<br />
x<br />
x<br />
x<br />
x<br />
x<br />
x<br />
x<br />
x<br />
x<br />
x<br />
x<br />
x<br />
x<br />
x<br />
x<br />
φ<br />
π<br />
φ<br />
π<br />
φ<br />
π<br />
φ<br />
=<br />
+<br />
−<br />
Γ<br />
= Γ<br />
+<br />
−<br />
−<br />
+<br />
−<br />
Γ<br />
Γ<br />
=<br />
+<br />
+<br />
−<br />
Γ<br />
+<br />
= Γ<br />
+<br />
−<br />
+<br />
−<br />
Γ<br />
=<br />
−<br />
Γ<br />
−<br />
Γ<br />
= −<br />
+<br />
−<br />
Γ