Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9721)

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=-17/4, b_1`>=-11/2

For fixed z and a₁=-17/4, b_1`=-11/2

http://functions.wolfram.com/07.22.03.9721.01

Input Form

HypergeometricPFQ[{-(17/4)}, {-(11/2), 23/4}, -z] == (19 (Sqrt[Pi] (-52239574574748185625 - 12231705266282502000 z - 1923413113125504000 z^2 - 310854644545536000 z^3 - 85753005391872000 z^4 + 54881923450798080 z^5 - 5575306509287424 z^6 + 249873681088512 z^7 - 5914169966592 z^8 + 68719476736 z^9) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) (4 Sqrt[z] (-17413191524916061875 + 3883081036915080000 z - 63774544138905600 z^2 - 6199380375552000 z^3 + 3502932211924992 z^4 - 351547372339200 z^5 + 15688173355008 z^6 - 370440929280 z^7 + 4294967296 z^8) Cos[2 Sqrt[z]] + (52239574574748185625 - 43490507613448896000 z + 3027933941403571200 z^2 - 10627509215232000 z^3 + 3828900741120000 z^4 - 364603867398144 z^5 + 15979492933632 z^6 - 373662154752 z^7 + 4294967296 z^8) Sin[2 Sqrt[z]])))/(1915155741539303424 z^(19/4))

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]