Did any king perform tapasya for a female child?
For example - like King Dasaratha performed the putrakamesthi yajña.
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There could be many examples, but two of them are as follows.:
Daksha Prajapati (Prajapati means Lord of the Prajas (People or Subjects) viz a King) did tapasya to get Mother Uma as his daughter.
Sri Shiva Maha Puranam. Chapter 12 - Dakṣa granted the boon. Section 2.2 - Rudra-saṃhitā (2): Satī-khaṇḍa.:
Dakṣa said:— 18. O wielder of great illusion, O mother of the universe, if you wish to grant me any boon please listen to my words with pleasure. Be pleased to fulfil my desire.
19. My lord and master Śiva has manifested Himself as Brahmā’s son in the name of Rudra. He is the perfect and full-fledged incarnation of the supreme soul.
20. You have not so far incarnated. Who will be His wife? Hence O Śivā, take an incarnation on the Earth and fascinate the great lord.
21. Excepting you, no other lady will ever be competent to enthral Him. Hence be born as my daughter and become Śiva’s consort.
22. Exhibiting your divine sports as this, O Goddess, you be the enchantress of Śiva, this is the only boon I crave of you. I speak out the truth to you.
23. This fulfils my own interests. Indeed it fulfils the interests of all the worlds as well as those of Brahmā, Viṣṇu and Śiva. Hence I have been induced by Brahmā in this direction.
Lord GiriRaaj Himalaya, the king of the mountains also did tapasya of Mother Uma to get her as his daughter.
Srimad Devi Bhahwatam MahaPuranam. Chapter 31 - On the Birth of Pārvatī in the House of Himālayās. Book 7.:
66-73. Vyāsa said :-- "O King (Janmajaya) ! Hearing the kind words of the Devī, the King of mountains was filled with love; and, with voice choked with feelings and with tears in his eyes spoke to the Goddess of the world, the Queen. of the three worlds. Thou hast raised me much higher, that Thou dost me so great a favour; otherwise where am I inert, and unmoving and where art Thou, of the nature of Existence, Intelligence and Bliss! It manifests the Greatness of Thy Glory. O Sinless One! My becoming the father of Thee indicates nothing less than the merits earned by me for doing, countless Aśvamedha sacrifices or for my endless Samādhi. Oh! What a favour hast Thou shewn towards me! Henceforth my unparalleled fame will be spread throughout the whole Universe of five original elements that "The Upholder of the Universe, the World Mother has become the daughter of this Himālayās! This man is blessed and fortunate!" Who can be so fortunate, virtuous and merited as he whose daughter She has become, Whose belly contains millions of Brahmāṇḍas! I cannot describe what pre-eminent heavens are intended for my Pitris, my family predecessors, wherein virtuous persons like myself are born. O Mother! O Parameśvarī! Now describe to me Thy Real Self as exemplified in all the Vedāntas; and also Jñāna with Bhakti approved by the Vedas in the same way that Thou hast shown already this favour to me, so that by That Knowledge I will be able to realise Thy Self.
I hope this clarifies your queries.
There are many such instances, like the Ashwapati did penance for a daughter (Savitri), Kushdwaja and Dharmadhwaja for Laxmi to be born as daughter (Vedavati & Tulasī), Daksha for Sati, Himavat and Mainavati for Parvati.
Other than these, Draupad and Devapanna got daughters out of their austerities too.(Thou they wished for sons.) Also, various manasik daughters were born from Tapobala, eg. Manasa form Kashyapa.
Shrimad Devi Mahabhagwat, 7th skanda Chapter 30 - On the birth of Gaurī, the seats of the Deity, and the distraction of Śiva
Dakṣa again asked :-- “O Devī! Let your birth be in my family. O Mother! I will, no doubt, consider myself as having then realised the fulfilment of my life. So, O Parameśvarī! Speak by Thy own mouth how Thy worship, Japam, meditation will be conducted as well the various fit places where they would be performed.”
Chapter 31 - On the Birth of Pārvatī in the House of Himālayās
Hearing the Dava’s words, Parameśvarī, with a graceful countenance, spoke to them, thus :-- "My Śaktī will incarnate as Gaurī in the house of Himālayās; She will be the wife of Śiva and will beget a son that will destroy Tāraka Demon and will serve your purpose. And your devotion will remain steadfast at My Lotus feet. Himālayās, too, is worshipping Me with his wholehearted devotion; so to take birth in his house is to my greatest liking; know this.
9th Skanda Chapter 15 - On the anecdote of Tulasí
Their kingdoms are lost; they have become destitute of all property, prosperity and they are now engaged in worshipping Mahā Lakṣmī. Mahā Lakṣmī will be born in parts of their two wives. Then again, by the grace of Lakṣmī, Dharmadhvaja and Kuśadhvaja will be prosperous and become great Kings.
Chapter 16 - On the incarnation of Mahā Lakṣmī in the house of Kuśadhvaja
Śrī Nārāyaṇa said :-- O Muni! Dharmadhvaja and Kuśadhvaja practised severe tapasyās and worshipped Lakṣmī. They then got separately their desired boons. By the boon of Mahā Lakṣmī, they became again the rulers of the earth. They acquired great religious merits and they also had their children. The wife of Kuśadhvaja was named Mālāvatī. After a long time, the chaste wife delivered one daughter, born of the parts of Kamalā
Chapter 17 - On the anecdote of Tulasī
However, by the Deva’s influence, she became pregnant and conceived for one hundred years. In the womb there was the incarnation of Lakṣmī; and the body’s lustre increased day by day. The holy wise men named Her Tulasī
Chapter 27 - On the birth, etc., of Sāvitrī
O King! I know your desire. Certainly I will give what you and your wife long for. Your chaste wife is anxious for a daughter, while you want a son. So, one after another, the desires of both of you will be fulfilled.” Thus saying, the Devī went to the Brahma Loka. The King also returned to his house. First a daughter was born to him. As the daughter was born, as if a second Lakṣmī was born after worshipping Sāvitrī, the King kept her name as Sāvitrī.
Chaitraratha Parva of Adiparva Mahabharata Drupad had 2 desires. First, that he have a son who would kill Drona and avenge the insult. Second, to have a daughter who would marrry Arjun, whose skills greatly impressed Drupad.
tAM chApi jAtAM sushroNIM vAguvAchAsharIriNI |
sarvayoShidvarA kRRiShNA kShayaM kShatraM ninIShati || 44||
surakAryamiyaM kAle kariShyati sumadhyamA |
asyA hetoH kShatriyANAM mahadutpatsyate bhayam || 45||
This dark-complexioned girl will be the first of all women, and she will be the cause of the destruction of many Kshatriyas. This slender-waisted one will, in time, accomplish the purpose of the gods, and along with her many a danger will overtake the Kauravas.
Skanda Puran, Section 3 - Revā-khaṇḍa, Chapter 169 - The Abduction of Kāmamohinī
He performed the Yajña dedicated to the Yajñapuruṣa and thereupon a daughter was born. She was radiant, beautiful and charming unto all the people.
Such a lovely maiden could be found neither in Devaloka nor in Gandharvaloka. Out of delight she was named Kāmapramodinī by her father.