About the Project
NIST

q-sine function

AdvancedHelp

(0.002 seconds)

4 matching pages

1: 17.3 q -Elementary and q -Special Functions
q -Sine Functions
17.3.3 sin q ( x ) = 1 2 i ( e q ( i x ) - e q ( - i x ) ) = n = 0 ( 1 - q ) 2 n + 1 ( - 1 ) n x 2 n + 1 ( q ; q ) 2 n + 1 ,
17.3.4 Sin q ( x ) = 1 2 i ( E q ( i x ) - E q ( - i x ) ) = n = 0 ( 1 - q ) 2 n + 1 q n ( 2 n + 1 ) ( - 1 ) n x 2 n + 1 ( q ; q ) 2 n + 1 .
2: 28.4 Fourier Series
28.4.3 se 2 n + 1 ( z , q ) = m = 0 B 2 m + 1 2 n + 1 ( q ) sin ( 2 m + 1 ) z ,
28.4.4 se 2 n + 2 ( z , q ) = m = 0 B 2 m + 2 2 n + 2 ( q ) sin ( 2 m + 2 ) z .
3: 28.6 Expansions for Small q
28.6.23 se 1 ( z , q ) = sin z - 1 8 q sin 3 z + 1 128 q 2 ( 2 3 sin 5 z + 2 sin 3 z - sin z ) - 1 1024 q 3 ( 1 9 sin 7 z + 8 9 sin 5 z - 1 3 sin 3 z - 2 sin z ) + ,
28.6.25 se 2 ( z , q ) = sin 2 z - 1 12 q sin 4 z + 1 128 q 2 ( 1 3 sin 6 z - 4 9 sin 2 z ) + .
4: 28.14 Fourier Series
28.14.3 se ν ( z , q ) = m = - c 2 m ν ( q ) sin ( ν + 2 m ) z ,