Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9030)

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`=9/2

http://functions.wolfram.com/07.22.03.9030.01

Input Form

HypergeometricPFQ[{-(21/4)}, {9/2, 5/4}, z] == ((4 z (-58615481925 + 17644173624000 z - 39027565088820 z^2 + 17546610312000 z^3 - 2061190010880 z^4 + 79228993536 z^5 - 1062469632 z^6 + 4194304 z^7) BesselI[1/4, Sqrt[z]]^2 - 12 Sqrt[z] (-97692469875 + 121572851400 z - 13134463060950 z^2 + 7926697769760 z^3 - 996702981120 z^4 + 39152762880 z^5 - 529399808 z^6 + 2097152 z^7) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + (-1465387048125 + 1693336144500 z - 3890331244800 z^2 + 110726960374800 z^3 - 64302428171520 z^4 + 8011205959680 z^5 - 313745080320 z^6 + 4237295616 z^7 - 16777216 z^8) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/(35132039296200 Sqrt[2] z^(9/4))

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,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]