Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.anrk)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a₁=11/2, a₂>=11/2

For fixed z and a₁=11/2, a₂=6, b₁>=-11/2

For fixed z and a₁=11/2, a₂=6, b₁=-11/2

http://functions.wolfram.com/07.25.03.anrk.01

Input Form

HypergeometricPFQ[{11/2, 6}, {-(11/2), -(3/2)}, z] == (1/442047375) (442047375 + 1768189500 z + 17878360500 z^2 - 204324120000 z^3 + 1042053012000 z^4 - 5279735260800 z^5 + 58077087868800 z^6 + 259770710707200 z^7 + 339540483744000 z^8 + 211975132723200 z^9 + 74864437401600 z^10 + 16269293174400 z^11 + 2277107280000 z^12 + 209894207040 z^13 + 12788775360 z^14 + 506843136 z^15 + 12493824 z^16 + 173056 z^17 + 1024 z^18) + (1/442047375) (32 E^z Sqrt[Pi] (3892112532000 z^(13/2) + 11676337596000 z^(15/2) + 13164498270000 z^(17/2) + 7605485118000 z^(19/2) + 2564796291750 z^(21/2) + 541149874650 z^(23/2) + 74257482915 z^(25/2) + 6751562895 z^(27/2) + 407380050 z^(29/2) + 16031400 z^(31/2) + 393120 z^(33/2) + 5424 z^(35/2) + 32 z^(37/2)) Erf[Sqrt[z]])

Standard Form

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MathML Form

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Rule 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},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁},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]