Sanskrit infinitive - formation

[pc2]

salutations,

we would like very much to know how is the formation of the root of the infinitive that precedes the inflected form of -tu.

for example:

शक्नोति कर्तुम् द्रष्टुम्
śaknoti kartum, draSTum. note: capital S and T are retroflex s and t, and should appear in the transliteration as s and t with underdot, but this is unfortunately not possible, because of the HTML limitation.
śaknoti kartum, draSTum - he can do, see.
in this case, ROOT-tu is the direct object of the verb śaknoti.

another example:
ईन्द्रम् चोदय दातवे मघम्
īndram codaya dātave magham - urge Indra to give bounty.

in this case, dā-tave is from the verb dā (to give) with -tu in the dative case (to the giving / to give) (compare with gurave (from root guru) - to the master).

भष्टुम् इच्चामि
bhaSTum icchāmi - I want to eat / I want "the eating".

एष्टवएष
eSTava_eSa (eSTave + eSa - Sandhi rules) - I ran away from the running away.

now here is the question:
how is the Infinitive root that comes before -tu or -itu is formed? for example:
eSTum = eS + tum, from the verb īS (to run away). how is this eS formed?

bhavitum = bhav + itum, from the root भू (bhū) - to be. how is bhav formed from bhū? is it like the present = bhū + guNa + o = bhoa = bhava? is it vrddhi?

now, an important note:
you don't need to explain in details about how the present and imperfect systems work, because we are already familiar with it. you can just think about explaining the Infinitive, and skip the basics, like explaining what is guNa and vrddhi, or Ánga, or the fact that Sanskrit has 10 verb classes/houses or Ganá-s.

best regards,

[pc2]

salutations,

we did some analysation of the infinitive form, and we think we discovered why it's like this. look:

the future is formed by simply the guNa of the word + sya or iSya. and, from that, we perceived that the infinitive is the same. the only complication that made we think it's irregular is the Sandhi combination rules, but it's very easy. look:

1st example: bhakS + guNa + tum = भष्टुम् bhaSTum, but it's not irregular, it's just the Sandhi acting.

2nd example: ii.s + guNa = eS + tum = एष्टुम् eSTum!

3rd example: bhuj + guNa = bhoj. bhoj + tum = भोक्तुम् bhoktum.

4th example: bhuu + guNa = bho + itum = भवितुम् bhavitum. simple!

5th and last comproving example: k.r + guNa = kar + tum = कर्तुम् kartum, and it's future = kar + iSya = करिष्यति kariSyati.

we are surely very satisfied, and we think this will also help many readers here with the same difficulty.

best regards,