Function note

BESSELI gives #NUM! just above 709.7, where the function is still finite

FUNC.BESSELI

FN-BESSELI-004: BESSELI gives #NUM! just above 709.7, where the function is still finite

Quirk · measured · recorded 2026-11-04

BESSELI returns a number at |x| = 709.7 and #NUM! at the next binary64 above it, although I0 there is about 2.48E306, well inside the binary64 range. Recorded for orders 0, 1, 2, 3, 10 and 100, and for negative x at orders 0 to 2.

Call and input routeInputsExcelCorrect valueRecorded in
BESSELI(709.7, 0)
cell-value2		x: 709.7
0x40862d999999999a
n: 0
0x0000000000000000		2.4788083687166675e+306
0x7f8c3d51558ee541		—Excel 16.0 build 20527, Windows 64-bit, AMD Ryzen 7 4800H
BESSELI(709.7000000000002, 0)
cell-value2		x: 709.7000000000002
0x40862d999999999b
n: 0
0x0000000000000000		#NUM!—Excel 16.0 build 20527, Windows 64-bit, AMD Ryzen 7 4800H
BESSELI(709.7000000000002, 1)
cell-value2		x: 709.7000000000002
0x40862d999999999b
n: 1
0x3ff0000000000000		#NUM!—Excel 16.0 build 20527, Windows 64-bit, AMD Ryzen 7 4800H

Basis: Adjacent-input readings at the boundary.

Inferred: That the same cut-off applies at every other order is inferred.

Evidence and capture sources

Machine-readable note records