On Laplace transforms near the origin

Author:
R. Wong

Journal:
Math. Comp. **29** (1975), 573-576

MSC:
Primary 44A10

DOI:
https://doi.org/10.1090/S0025-5718-1975-0367564-1

MathSciNet review:
0367564

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let be locally integrable on and let denote the Laplace transform of . In this note, we prove that if as , where , then as in , the being constants.

**[1]**C. J. BOUWKAMP, "Note on an asymptotic expansion,"*Indiana Univ. Math. J.*, v. 21, 1971, pp. 547-549. MR**0291703 (45:794)****[2]**RICHARD A. HANDELSMAN & JOHN S. LEW, "Asymptotic expansion of Laplace transforms near the origin,"*SIAM J. Math. Anal.*, v. 1, 1970, pp. 118-129. MR**41**#4142. MR**0259504 (41:4142)****[3]**R. WONG, "On a Laplace integral involving logarithms,"*SIAM J. Math. Anal.*, v. 1, 1970, pp. 360-364. MR**43**#7842. MR**0282129 (43:7842)**

Retrieve articles in *Mathematics of Computation*
with MSC:
44A10

Retrieve articles in all journals with MSC: 44A10

Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1975-0367564-1

Keywords:
Laplace transform,
asymptotic expansion,
Ramanujan function

Article copyright:
© Copyright 1975
American Mathematical Society