Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8856)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For rational parameters with larger denominators and fixed z

For fixed z and a₁=-21/4, b_1`>=-11/2

For fixed z and a₁=-21/4, b_1`=1/2

http://functions.wolfram.com/07.22.03.8856.01

Input Form

HypergeometricPFQ[{-(21/4)}, {1/2, 23/4}, z] == (-4 z^(1/4) (473793336560919375 + 631724448747892500 Sqrt[z] + 208097465469894000 z - 107587805276952000 z^(3/2) - 39070040929920000 z^2 + 65046338413056000 z^(5/2) - 7884404656128000 z^3 - 69382760973926400 z^(7/2) + 113535427048243200 z^4 - 794432292795187200 z^(9/2) - 178387064664883200 z^5 + 787244904559411200 z^(11/2) + 28200851566755840 z^6 - 116273970696683520 z^(13/2) - 1213226255646720 z^7 + 4903413837987840 z^(15/2) + 17072495001600 z^8 - 68496138436608 z^(17/2) - 68719476736 z^9 + 274877906944 z^(19/2) + E^(4 Sqrt[z]) (-473793336560919375 + 631724448747892500 Sqrt[z] - 208097465469894000 z - 107587805276952000 z^(3/2) + 39070040929920000 z^2 + 65046338413056000 z^(5/2) + 7884404656128000 z^3 - 69382760973926400 z^(7/2) - 113535427048243200 z^4 - 794432292795187200 z^(9/2) + 178387064664883200 z^5 + 787244904559411200 z^(11/2) - 28200851566755840 z^6 - 116273970696683520 z^(13/2) + 1213226255646720 z^7 + 4903413837987840 z^(15/2) - 17072495001600 z^8 - 68496138436608 z^(17/2) + 68719476736 z^9 + 274877906944 z^(19/2))) - E^(2 Sqrt[z]) Sqrt[2 Pi] (-473793336560919375 + 297282093528420000 z - 149680494643680000 z^2 + 101370917007360000 z^3 - 189225711747072000 z^4 - 3633133665543782400 z^5 + 3229452147150028800 z^6 - 468673327477555200 z^7 + 19664615138918400 z^8 - 274190712176640 z^9 + 1099511627776 z^10) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] (-473793336560919375 + 297282093528420000 z - 149680494643680000 z^2 + 101370917007360000 z^3 - 189225711747072000 z^4 - 3633133665543782400 z^5 + 3229452147150028800 z^6 - 468673327477555200 z^7 + 19664615138918400 z^8 - 274190712176640 z^9 + 1099511627776 z^10) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z])/ (7979815589747097600 z^(19/4))

Standard Form

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MathML Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]