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

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=5, b₁>=-11/2

For fixed z and a₁=7/2, a₂=5, b₁=-7/2

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

Input Form

HypergeometricPFQ[{7/2, 5}, {-(7/2), -(7/2)}, z] == (1/496125) (496125 + 708750 z + 1530900 z^2 + 8731800 z^3 + 454053600 z^4 + 18637819200 z^5 + 75072816000 z^6 + 99874091520 z^7 + 61346096640 z^8 + 20242678080 z^9 + 3878656320 z^10 + 447669600 z^11 + 31285792 z^12 + 1284544 z^13 + 28288 z^14 + 256 z^15) + (1/496125) (16 E^z Sqrt[Pi] (183783600 z^(9/2) + 2355771600 z^(11/2) + 6782643000 z^(13/2) + 7734547800 z^(15/2) + 4372996950 z^(17/2) + 1374495570 z^(19/2) + 255520545 z^(21/2) + 28919025 z^(23/2) + 1994640 z^(25/2) + 81160 z^(27/2) + 1776 z^(29/2) + 16 z^(31/2)) 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]