On a remarkable formula of Ramanujan
A simple proof of Ramanujan’s formula for the Fourier transform of |Γ ( a + it )| 2 is given where a is fixed and has positive real part and t is real. The result is extended to other values of a by solving an inhomogeneous ODE, and we use it to calculate the jump across the imaginary axis.
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| Veröffentlicht in: | Archiv der Mathematik 2012-08, Vol.99 (2), p.125-135 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | A simple proof of Ramanujan’s formula for the Fourier transform of |Γ (
a
+
it
)|
2
is given where
a
is fixed and has positive real part and
t
is real. The result is extended to other values of
a
by solving an inhomogeneous ODE, and we use it to calculate the jump across the imaginary axis. |
|---|---|
| ISSN: | 0003-889X 1420-8938 |
| DOI: | 10.1007/s00013-012-0416-9 |