Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.1178)

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=3/2, b₁>=-11/2

For fixed z and a₁=-11/2, a₂=3/2, b₁=-3/2

http://functions.wolfram.com/07.25.03.1178.01

Input Form

HypergeometricPFQ[{-(11/2), 3/2}, {-(3/2), 5}, z] == (1/(218243025 z^2)) (32 E^(z/2) (-7203735 - 6767145 z + 3534300 z^2 + 3783780 z^3 + 10376400 z^4 - 23578704 z^5 + 8969472 z^6 - 1100800 z^7 + 40960 z^8) BesselI[0, z/2]) - (1/(218243025 z^3)) (32 E^(z/2) (-28814940 - 27068580 z - 14043645 z^2 - 2079000 z^3 - 1862340 z^4 - 2727936 z^5 - 16137552 z^6 + 7930112 z^7 - 1059840 z^8 + 40960 z^9) BesselI[1, z/2])

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]