Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8808)

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/07.22.03.8808.01

Input Form

HypergeometricPFQ[{-(21/4)}, {-(1/2), 23/4}, z] == (19 (4 z^(1/4) (-523666319356805625 - 698221759142407500 Sqrt[z] - 292588165735866000 z + 35465232210408000 z^(3/2) + 39447958822272000 z^2 - 26009643179520000 z^(5/2) - 5038905231360000 z^3 + 23570220235161600 z^(7/2) - 19254546107596800 z^4 + 59722256705126400 z^(9/2) - 23968657598054400 z^5 + 120423056198860800 z^(11/2) + 10172417641021440 z^6 - 42655117391953920 z^(13/2) - 699118670315520 z^7 + 2836160179077120 z^(15/2) + 13464722472960 z^8 - 54065048322048 z^(17/2) - 68719476736 z^9 + 274877906944 z^(19/2) + E^(4 Sqrt[z]) (523666319356805625 - 698221759142407500 Sqrt[z] + 292588165735866000 z + 35465232210408000 z^(3/2) - 39447958822272000 z^2 - 26009643179520000 z^(5/2) + 5038905231360000 z^3 + 23570220235161600 z^(7/2) + 19254546107596800 z^4 + 59722256705126400 z^(9/2) + 23968657598054400 z^5 + 120423056198860800 z^(11/2) - 10172417641021440 z^6 - 42655117391953920 z^(13/2) + 699118670315520 z^7 + 2836160179077120 z^(15/2) - 13464722472960 z^8 - 54065048322048 z^(17/2) + 68719476736 z^9 + 274877906944 z^(19/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] (523666319356805625 - 265989241578060000 z + 102412970019360000 z^2 - 48017802792960000 z^3 + 49796239933440000 z^4 + 191217561344409600 z^5 + 509913496918425600 z^6 - 172669120649625600 z^7 + 11384777185689600 z^8 - 216466351718400 z^9 + 1099511627776 z^10) Erf[Sqrt[2] z^(1/4)] - E^(2 Sqrt[z]) Sqrt[2 Pi] (523666319356805625 - 265989241578060000 z + 102412970019360000 z^2 - 48017802792960000 z^3 + 49796239933440000 z^4 + 191217561344409600 z^5 + 509913496918425600 z^6 - 172669120649625600 z^7 + 11384777185689600 z^8 - 216466351718400 z^9 + 1099511627776 z^10) Erfi[Sqrt[2] z^(1/4)]))/E^(2 Sqrt[z])/ (15959631179494195200 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]