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

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=7/2, a₂>=7/2

For fixed z and a₁=7/2, a₂=6, b₁>=-11/2

For fixed z and a₁=7/2, a₂=6, b₁=-11/2

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

Input Form

HypergeometricPFQ[{7/2, 6}, {-(11/2), -(7/2)}, z] == (1/245581875) (245581875 + 267907500 z + 375070500 z^2 + 1047816000 z^3 + 12259447200 z^4 - 245188944000 z^5 + 5094481392000 z^6 + 39199792665600 z^7 + 73806116025600 z^8 + 60933353564160 z^9 + 26986621132800 z^10 + 7090909862400 z^11 + 1168423226880 z^12 + 124240616640 z^13 + 8593484736 z^14 + 381639680 z^15 + 10429440 z^16 + 158720 z^17 + 1024 z^18) + (1/245581875) (32 E^z Sqrt[Pi] (424594094400 z^(13/2) + 1934261985600 z^(15/2) + 3004766377200 z^(17/2) + 2247376395600 z^(19/2) + 939707508600 z^(21/2) + 238193396280 z^(23/2) + 38333718045 z^(25/2) + 4011214515 z^(27/2) + 274352610 z^(29/2) + 12086760 z^(31/2) + 328384 z^(33/2) + 4976 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]