I looking examples generated explosion sound.
And theory,formules how do this.

you can generate explosion with a bunch of oscillators, modulators and envoloppe generator.

you can search for any sound synthesis software, and look how they will generate your explosion.

for example, with a sytrus synth, you can play with knobs, until you find what you find convenient as an explosion sound. then, you just have to implement the synth with all elements i told you before.

https://www.kvraudio.com/product/sytrus-by-image-line

this synth is the most versatile i know and you can even find presets of explosions.

after, you need a sound analysis to get the components.

something like that.

after trying...

you need a squarish ocscillator in descending pitch, shaped in a capacitor discharge enveloppe, passing through a reverb.

I using xaudio2 and generating sounds for my games.
I want generating explosion sound and not using any files wav or mp3.

yes, i get it. but all theses files are examples to show you the result, and how to make it using basic effects.

after, you just have to code the effects and it's ok.

if i should make sound synths, i will probably start by doing a periodic clock, something like 100kHz or more standard tick.

then, use the clock value to generate the signal using any formula, like sinus, triangle, square, and so on.
interpolate the signals to get clean curves because my sound generation couldn't be synch with the main clock, and will never have a stable resolution in time.

and then, send it to a sound buffer that will be played in loops by the sound driver.